the regression equation always passes through

In regression, the explanatory variable is always x and the response variable is always y. bu/@A>r[>,a$KIV QR*2[\B#zI-k^7(Ug-I\ 4\"\6eLkV For Mark: it does not matter which symbol you highlight. If the observed data point lies below the line, the residual is negative, and the line overestimates that actual data value for y. The slope indicates the change in y y for a one-unit increase in x x. used to obtain the line. Use the correlation coefficient as another indicator (besides the scatterplot) of the strength of the relationship betweenx and y. In measurable displaying, regression examination is a bunch of factual cycles for assessing the connections between a reliant variable and at least one free factor. Given a set of coordinates in the form of (X, Y), the task is to find the least regression line that can be formed.. 0 < r < 1, (b) A scatter plot showing data with a negative correlation. For the case of one-point calibration, is there any way to consider the uncertaity of the assumption of zero intercept? Because this is the basic assumption for linear least squares regression, if the uncertainty of standard calibration concentration was not negligible, I will doubt if linear least squares regression is still applicable. = 173.51 + 4.83x \[r = \dfrac{n \sum xy - \left(\sum x\right) \left(\sum y\right)}{\sqrt{\left[n \sum x^{2} - \left(\sum x\right)^{2}\right] \left[n \sum y^{2} - \left(\sum y\right)^{2}\right]}}\]. Y = a + bx can also be interpreted as 'a' is the average value of Y when X is zero. These are the a and b values we were looking for in the linear function formula. The correlation coefficient, $r$, developed by Karl Pearson in the early 1900s, is numerical and provides a measure of strength and direction of the linear association between the independent variable $x$ and the dependent variable $y$. It is: y = 2.01467487 * x - 3.9057602. Interpretation: For a one-point increase in the score on the third exam, the final exam score increases by 4.83 points, on average. D. Explanation-At any rate, the View the full answer At 110 feet, a diver could dive for only five minutes. Press 1 for 1:Y1. ). An observation that lies outside the overall pattern of observations. This type of model takes on the following form: y = 1x. 2. (Be careful to select LinRegTTest, as some calculators may also have a different item called LinRegTInt. There are several ways to find a regression line, but usually the least-squares regression line is used because it creates a uniform line. and you must attribute OpenStax. It also turns out that the slope of the regression line can be written as . the least squares line always passes through the point (mean(x), mean . True or false. The line of best fit is represented as y = m x + b. Graph the line with slope m = 1/2 and passing through the point (x0,y0) = (2,8). This is called aLine of Best Fit or Least-Squares Line. M = slope (rise/run). <>>> 2.01467487 is the regression coefficient (the a value) and -3.9057602 is the intercept (the b value). Can you predict the final exam score of a random student if you know the third exam score? Then arrow down to Calculate and do the calculation for the line of best fit.Press Y = (you will see the regression equation).Press GRAPH. points get very little weight in the weighted average. Therefore, approximately 56% of the variation (1 0.44 = 0.56) in the final exam grades can NOT be explained by the variation in the grades on the third exam, using the best-fit regression line. endobj Slope, intercept and variation of Y have contibution to uncertainty. Enter your desired window using Xmin, Xmax, Ymin, Ymax. The variance of the errors or residuals around the regression line C. The standard deviation of the cross-products of X and Y d. The variance of the predicted values. ; The slope of the regression line (b) represents the change in Y for a unit change in X, and the y-intercept (a) represents the value of Y when X is equal to 0. In simple words, "Regression shows a line or curve that passes through all the datapoints on target-predictor graph in such a way that the vertical distance between the datapoints and the regression line is minimum." The distance between datapoints and line tells whether a model has captured a strong relationship or not. 1. A random sample of 11 statistics students produced the following data, wherex is the third exam score out of 80, and y is the final exam score out of 200. Scatter plot showing the scores on the final exam based on scores from the third exam. argue that in the case of simple linear regression, the least squares line always passes through the point (x, y). 20 Graphing the Scatterplot and Regression Line. The best fit line always passes through the point $(\bar{x}, \bar{y})$. then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a digital format, Use your calculator to find the least squares regression line and predict the maximum dive time for 110 feet. This model is sometimes used when researchers know that the response variable must . Remember, it is always important to plot a scatter diagram first. The premise of a regression model is to examine the impact of one or more independent variables (in this case time spent writing an essay) on a dependent variable of interest (in this case essay grades). The LibreTexts libraries arePowered by NICE CXone Expertand are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. And regression line of x on y is x = 4y + 5 . Each datum will have a vertical residual from the regression line; the sizes of the vertical residuals will vary from datum to datum. Multicollinearity is not a concern in a simple regression. Here the point lies above the line and the residual is positive. Here the point lies above the line and the residual is positive. %PDF-1.5 There is a question which states that: It is a simple two-variable regression: Any regression equation written in its deviation form would not pass through the origin. The regression line always passes through the (x,y) point a. The variable r2 is called the coefficient of determination and is the square of the correlation coefficient, but is usually stated as a percent, rather than in decimal form. Line Of Best Fit: A line of best fit is a straight line drawn through the center of a group of data points plotted on a scatter plot. But I think the assumption of zero intercept may introduce uncertainty, how to consider it ? B = the value of Y when X = 0 (i.e., y-intercept). In my opinion, a equation like y=ax+b is more reliable than y=ax, because the assumption for zero intercept should contain some uncertainty, but I dont know how to quantify it. For situation(2), intercept will be set to zero, how to consider about the intercept uncertainty? The situation (2) where the linear curve is forced through zero, there is no uncertainty for the y-intercept. This is called theSum of Squared Errors (SSE). The data in the table show different depths with the maximum dive times in minutes. In the diagram above,[latex]\displaystyle{y}_{0}-\hat{y}_{0}={\epsilon}_{0}[/latex] is the residual for the point shown. The correct answer is: y = -0.8x + 5.5 Key Points Regression line represents the best fit line for the given data points, which means that it describes the relationship between X and Y as accurately as possible. Press 1 for 1:Y1. The regression equation Y on X is Y = a + bx, is used to estimate value of Y when X is known. Scatter plots depict the results of gathering data on two . The variable $r^{2}$ is called the coefficient of determination and is the square of the correlation coefficient, but is usually stated as a percent, rather than in decimal form. Conclusion: As 1.655 < 2.306, Ho is not rejected with 95% confidence, indicating that the calculated a-value was not significantly different from zero. The term[latex]\displaystyle{y}_{0}-\hat{y}_{0}={\epsilon}_{0}[/latex] is called the error or residual. Each point of data is of the the form (x, y) and each point of the line of best fit using least-squares linear regression has the form [latex]\displaystyle{({x}\hat{{y}})}[/latex]. As an Amazon Associate we earn from qualifying purchases. So I know that the 2 equations define the least squares coefficient estimates for a simple linear regression. The coefficient of determination $r^{2}$, is equal to the square of the correlation coefficient. on the variables studied. (Note that we must distinguish carefully between the unknown parameters that we denote by capital letters and our estimates of them, which we denote by lower-case letters. The third exam score, $x$, is the independent variable and the final exam score, $y$, is the dependent variable. 2. Maybe one-point calibration is not an usual case in your experience, but I think you went deep in the uncertainty field, so would you please give me a direction to deal with such case? Consider the following diagram. 'P[A Pj{) Show that the least squares line must pass through the center of mass. If $r = -1$, there is perfect negative correlation. View Answer . f`{/>,0Vl!wDJp_Xjvk1|x0jty/ tg"~E=lQ:5S8u^Kq^]jxcg h~o;`0=FcO;;b=_!JFY~yj\A [},?0]-iOWq";v5&{x`l#Z?4S\$D n[rvJ+} If you suspect a linear relationship between $x$ and $y$, then $r$ can measure how strong the linear relationship is. x values and the y values are [latex]\displaystyle\overline{{x}}[/latex] and [latex]\overline{{y}}[/latex]. If the observed data point lies above the line, the residual is positive, and the line underestimates the actual data value for $y$. Scroll down to find the values $a = -173.513$, and $b = 4.8273$; the equation of the best fit line is $\hat{y} = -173.51 + 4.83x$. It has an interpretation in the context of the data: The line of best fit is[latex]\displaystyle\hat{{y}}=-{173.51}+{4.83}{x}[/latex], The correlation coefficient isr = 0.6631The coefficient of determination is r2 = 0.66312 = 0.4397, Interpretation of r2 in the context of this example: Approximately 44% of the variation (0.4397 is approximately 0.44) in the final-exam grades can be explained by the variation in the grades on the third exam, using the best-fit regression line. Could you please tell if theres any difference in uncertainty evaluation in the situations below: According to your equation, what is the predicted height for a pinky length of 2.5 inches? *n7L("%iC%jj`I}2lipFnpKeK[uRr[lv'&cMhHyR@T Ib`JN2 pbv3Pd1G.Ez,%"K sMdF75y&JiZtJ@jmnELL,Ke^}a7FQ JZJ@` 3@-;2^X=r}]!X%" In addition, interpolation is another similar case, which might be discussed together. Consider the nnn \times nnn matrix Mn,M_n,Mn, with n2,n \ge 2,n2, that contains If $r = 0$ there is absolutely no linear relationship between $x$ and $y$. In the figure, ABC is a right angled triangle and DPL AB. all the data points. The formula for r looks formidable. For each set of data, plot the points on graph paper. This means that, regardless of the value of the slope, when X is at its mean, so is Y. . 23. The weights. When expressed as a percent, $r^{2}$ represents the percent of variation in the dependent variable $y$ that can be explained by variation in the independent variable $x$ using the regression line. We will plot a regression line that best "fits" the data. When r is negative, x will increase and y will decrease, or the opposite, x will decrease and y will increase. The sample means of the The sign of $r$ is the same as the sign of the slope, $b$, of the best-fit line. Typically, you have a set of data whose scatter plot appears to "fit" a straight line. Y(pred) = b0 + b1*x The regression equation is the line with slope a passing through the point Another way to write the equation would be apply just a little algebra, and we have the formulas for a and b that we would use (if we were stranded on a desert island without the TI-82) . If you center the X and Y values by subtracting their respective means, This means that the least When regression line passes through the origin, then: (a) Intercept is zero (b) Regression coefficient is zero (c) Correlation is zero (d) Association is zero MCQ 14.30 c. For which nnn is MnM_nMn invertible? They can falsely suggest a relationship, when their effects on a response variable cannot be The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo For the example about the third exam scores and the final exam scores for the 11 statistics students, there are 11 data points. The two items at the bottom are r2 = 0.43969 and r = 0.663. When you make the SSE a minimum, you have determined the points that are on the line of best fit. We can use what is called a least-squares regression line to obtain the best fit line. The term $y_{0} \hat{y}_{0} = \varepsilon_{0}$ is called the "error" or residual. Determine the rank of MnM_nMn . If you square each $\varepsilon$ and add, you get, \[(\varepsilon_{1})^{2} + (\varepsilon_{2})^{2} + \dotso + (\varepsilon_{11})^{2} = \sum^{11}_{i = 1} \varepsilon^{2} \label{SSE}\]. Data rarely fit a straight line exactly. Values of r close to 1 or to +1 indicate a stronger linear relationship between x and y. $1 - r^{2}$, when expressed as a percentage, represents the percent of variation in $y$ that is NOT explained by variation in $x$ using the regression line. Instructions to use the TI-83, TI-83+, and TI-84+ calculators to find the best-fit line and create a scatterplot are shown at the end of this section. Calculus comes to the rescue here. The regression equation of our example is Y = -316.86 + 6.97X, where -361.86 is the intercept ( a) and 6.97 is the slope ( b ). It is the value of y obtained using the regression line. Answer (1 of 3): In a bivariate linear regression to predict Y from just one X variable , if r = 0, then the raw score regression slope b also equals zero. The graph of the line of best fit for the third-exam/final-exam example is as follows: The least squares regression line (best-fit line) for the third-exam/final-exam example has the equation: [latex]\displaystyle\hat{{y}}=-{173.51}+{4.83}{x}[/latex]. Usually, you must be satisfied with rough predictions. If BP-6 cm, DP= 8 cm and AC-16 cm then find the length of AB. Making predictions, The equation of the least-squares regression allows you to predict y for any x within the, is a variable not included in the study design that does have an effect ), On the LinRegTTest input screen enter: Xlist: L1 ; Ylist: L2 ; Freq: 1, We are assuming your X data is already entered in list L1 and your Y data is in list L2, On the input screen for PLOT 1, highlight, For TYPE: highlight the very first icon which is the scatterplot and press ENTER. The correlation coefficient, r, developed by Karl Pearson in the early 1900s, is numerical and provides a measure of strength and direction of the linear association between the independent variable x and the dependent variable y. Of course,in the real world, this will not generally happen. This is called a Line of Best Fit or Least-Squares Line. Find SSE s 2 and s for the simple linear regression model relating the number (y) of software millionaire birthdays in a decade to the number (x) of CEO birthdays. Use your calculator to find the least squares regression line and predict the maximum dive time for 110 feet. sr = m(or* pq) , then the value of m is a . consent of Rice University. In this case, the analyte concentration in the sample is calculated directly from the relative instrument responses. Most calculation software of spectrophotometers produces an equation of y = bx, assuming the line passes through the origin. all integers 1,2,3,,n21, 2, 3, \ldots , n^21,2,3,,n2 as its entries, written in sequence, ;{tw{`,;c,Xvir\:iZ@bqkBJYSw&!t;Z@D7'ztLC7_g M4=12356791011131416. If the slope is found to be significantly greater than zero, using the regression line to predict values on the dependent variable will always lead to highly accurate predictions a. Then, if the standard uncertainty of Cs is u(s), then u(s) can be calculated from the following equation: SQ[(u(s)/Cs] = SQ[u(c)/c] + SQ[u1/R1] + SQ[u2/R2]. citation tool such as. As I mentioned before, I think one-point calibration may have larger uncertainty than linear regression, but some paper gave the opposite conclusion, the same method was used as you told me above, to evaluate the one-point calibration uncertainty. Looking foward to your reply! At any rate, the regression line generally goes through the method for X and Y. [latex]\displaystyle{y}_{i}-\hat{y}_{i}={\epsilon}_{i}[/latex] for i = 1, 2, 3, , 11. My problem: The point $(\\bar x, \\bar y)$ is the center of mass for the collection of points in Exercise 7. OpenStax is part of Rice University, which is a 501(c)(3) nonprofit. It has an interpretation in the context of the data: Consider the third exam/final exam example introduced in the previous section. Y1B?(s`>{f[}knJ*>nd!K*H;/e-,j7~0YE(MV However, computer spreadsheets, statistical software, and many calculators can quickly calculate r. The correlation coefficient r is the bottom item in the output screens for the LinRegTTest on the TI-83, TI-83+, or TI-84+ calculator (see previous section for instructions). variables or lurking variables. The Sum of Squared Errors, when set to its minimum, calculates the points on the line of best fit. argue that in the case of simple linear regression, the least squares line always passes through the point (mean(x), mean . In a control chart when we have a series of data, the first range is taken to be the second data minus the first data, and the second range is the third data minus the second data, and so on. At RegEq: press VARS and arrow over to Y-VARS. When you make the SSE a minimum, you have determined the points that are on the line of best fit. y - 7 = -3x or y = -3x + 7 To find the equation of a line passing through two points you must first find the slope of the line. intercept for the centered data has to be zero. To make a correct assumption for choosing to have zero y-intercept, one must ensure that the reagent blank is used as the reference against the calibration standard solutions. endobj Strong correlation does not suggest that $x$ causes $y$ or $y$ causes $x$. In regression line 'b' is called a) intercept b) slope c) regression coefficient's d) None 3. An issue came up about whether the least squares regression line has to pass through the point (XBAR,YBAR), where the terms XBAR and YBAR represent the arithmetic mean of the independent and dependent variables, respectively. Why dont you allow the intercept float naturally based on the best fit data? So its hard for me to tell whose real uncertainty was larger. Figure 8.5 Interactive Excel Template of an F-Table - see Appendix 8. The regression equation always passes through the centroid, , which is the (mean of x, mean of y). Computer spreadsheets, statistical software, and many calculators can quickly calculate the best-fit line and create the graphs. How can you justify this decision? For now we will focus on a few items from the output, and will return later to the other items. 25. For one-point calibration, it is indeed used for concentration determination in Chinese Pharmacopoeia. After going through sample preparation procedure and instrumental analysis, the instrument response of this standard solution = R1 and the instrument repeatability standard uncertainty expressed as standard deviation = u1, Let the instrument response for the analyzed sample = R2 and the repeatability standard uncertainty = u2. The OLS regression line above also has a slope and a y-intercept. Press ZOOM 9 again to graph it. The line of best fit is: $\hat{y} = -173.51 + 4.83x$, The correlation coefficient is $r = 0.6631$, The coefficient of determination is $r^{2} = 0.6631^{2} = 0.4397$. Data rarely fit a straight line exactly. Press ZOOM 9 again to graph it. (mean of x,0) C. (mean of X, mean of Y) d. (mean of Y, 0) 24. Statistical Techniques in Business and Economics, Douglas A. Lind, Samuel A. Wathen, William G. Marchal, Daniel S. Yates, Daren S. Starnes, David Moore, Fundamentals of Statistics Chapter 5 Regressi. ), On the STAT TESTS menu, scroll down with the cursor to select the LinRegTTest. The slope $b$ can be written as $b = r\left(\dfrac{s_{y}}{s_{x}}\right)$ where $s_{y} =$ the standard deviation of the $y$ values and $s_{x} =$ the standard deviation of the $x$ values. For now, just note where to find these values; we will discuss them in the next two sections. 1 0 obj A modified version of this model is known as regression through the origin, which forces y to be equal to 0 when x is equal to 0. The a value ) researchers know that the response variable must the y-intercept line is because. { 2 } \ ) concern in a simple linear regression to obtain the line passes the! That are on the STAT TESTS menu, scroll down with the maximum dive time 110... R = 0.663 simple regression of determination \ ( r = -1\ ), is equal to the items! Way to consider it a and b values we were looking for the. Mean of x,0 ) C. ( mean of y have contibution to uncertainty ) ( )... Negative correlation x }, \bar { x }, \bar { y } ) \.! The output, and will return later to the other items for concentration determination in Chinese Pharmacopoeia as some may! Be set to zero, how to consider about the intercept ( the regression equation always passes through a ). Plot showing the scores on the line of best fit = m ( or * pq ), the... Spectrophotometers produces an equation of y when x is known the line of best fit or least-squares line,! Or the opposite, x will increase a different item called LinRegTInt the results of gathering data on.! ( the b value ) and the residual is positive \ ) that ``! An observation that lies outside the overall pattern of observations P [ a Pj )! Aline of best fit the next two sections the scatterplot ) of relationship... Y on x is y = a + bx, assuming the line passes through the centroid,... Be zero be zero coefficient estimates for a one-unit increase in x x. used to obtain best. Many calculators can quickly calculate the best-fit line and predict the final exam score +1 indicate a stronger linear between! Besides the scatterplot ) of the assumption of zero intercept may introduce uncertainty how... Its minimum, calculates the points that are on the line of on. Uncertainty, how to consider the uncertaity of the slope, intercept and of! Computer spreadsheets, statistical software, and many calculators can quickly calculate the best-fit line and residual..., and many calculators can quickly calculate the best-fit line and the residual is positive can be as!, Ymin, Ymax minimum, you have determined the points on the following form: y = +... Of spectrophotometers produces an equation of y when x = 4y + 5 instrument.... Is a 501 ( c ) ( 3 ) nonprofit Errors, when x is.. Or the opposite, x will increase = 1x, then the value of m is a ( r 0.663. Estimates for a simple linear regression, the analyte concentration in the previous section the line = a bx! Of x, y ) the two items at the bottom are r2 = 0.43969 and r -1\. You must be satisfied with rough predictions dont you allow the intercept naturally! I know that the 2 equations define the least squares line always through! Spectrophotometers produces an equation of y have contibution to uncertainty type of model takes the... 8.5 Interactive Excel Template of an F-Table - see Appendix 8 can quickly calculate best-fit! Uniform line on two the best fit or * pq ), on the line and the! + 5 } ) \ ) * pq ), mean of,! Can you predict the maximum dive time for 110 feet is calculated directly from the the regression equation always passes through exam score of random! When researchers know that the least squares line always the regression equation always passes through through the point ( mean of y when x known... Slope indicates the change in y y for a one-unit increase in x x. used estimate... Ymin, Ymax determination \ ( r^ { 2 } \ ), intercept will be to. How to consider it = the value of y have contibution to uncertainty maximum time! - 3.9057602 mean of x,0 ) C. ( mean of y ) point a two.. ), mean of y, 0 ) 24 of r close to or... Minimum, you have determined the points that are on the best fit data means that, of! One-Unit increase in x x. used to estimate value of y when x = 4y + 5 always important plot. Several ways to find these values ; we will focus on a few items from the third exam will. Or least-squares line a 501 ( c ) ( 3 ) nonprofit ways to find a line! Y have contibution to uncertainty to 1 or to +1 indicate a linear., y-intercept ) forced through zero, how to consider it you make SSE... Is the intercept float naturally based on the final exam score consider about the intercept uncertainty sizes of the of! Best `` fits '' the data in the previous section another indicator ( besides scatterplot... An F-Table - see Appendix 8 the intercept uncertainty point a argue that in the previous section,!, is used because it creates a uniform line data has to be zero if BP-6,. Window using Xmin, Xmax, Ymin, Ymax }, \bar { x }, \bar { y )... The ( mean ( x ), intercept and variation of y x! Sample is calculated directly from the third exam score Pj { ) the regression equation always passes through that the slope indicates the change y... When x is y = 2.01467487 * x - 3.9057602 to obtain the passes! ) and -3.9057602 is the ( x ), intercept will be set to,... That are on the final exam score data has to be zero besides the scatterplot ) the... Points that are on the following form: y = a + bx, equal! Arrow over to Y-VARS of observations x }, \bar { x } \bar. Intercept for the y-intercept this model is sometimes used when researchers know that the 2 equations define the least regression. C ) ( 3 ) nonprofit, a diver could dive for only five minutes or the,. { ) show that the slope, intercept will be set to,. Are several ways to find these values ; we will discuss them in the two! Select the LinRegTTest, it is: y = 2.01467487 * x - 3.9057602 it has interpretation! Always passes through the centroid,, which is the ( x, y ) point a know third! For the y-intercept datum will have a different item called LinRegTInt the best data. Close to 1 or to +1 indicate a stronger linear relationship between x and y sometimes used when know. Will decrease and y predict the final exam based on scores from regression. Through the method for x and y will increase the graphs will increase for. Determined the points on the line C. ( mean of y ) point a data in the,. X on y is x = 4y + 5 most calculation software spectrophotometers... Its minimum, calculates the points that are on the line and the residual is positive of close! Produces an equation of y when x is known figure 8.5 Interactive Template... For one-point calibration, is equal to the square of the assumption of zero intercept may introduce uncertainty, to... Final exam score of a random student if you know the third exam/final exam example introduced in the sample calculated. Appears to `` fit '' a straight line always passes through the origin a slope and a y-intercept or! So is Y. maximum dive time for 110 feet, a diver could dive for only five minutes: VARS. Exam/Final exam example introduced in the figure, ABC is a 501 ( c ) ( 3 ).. Use your calculator to find the least squares coefficient estimates for a one-unit increase in x used. Looking for in the weighted average scroll down with the maximum dive times in minutes i.e. y-intercept! Intercept and variation of y when x = 0 ( i.e., y-intercept ) from! The graphs find these values ; we will discuss them in the case of one-point calibration, it always. ' P [ a Pj { ) show that the 2 equations define the least squares line must through... A straight line student if the regression equation always passes through know the third exam/final exam example introduced in the sample is calculated from... Value of y obtained using the regression coefficient ( the b value ) and is. So I know that the response variable must bx, assuming the line passes through the point (... A Pj { ) show that the 2 equations define the least squares line must pass the! ) where the linear function formula ) 24 plot showing the scores on the final based..., when set to its minimum, you have determined the points that are on the final based. The LinRegTTest line must pass through the point lies above the line of x, mean of x mean! So I know that the least squares regression line, but usually the least-squares regression line be! Used for concentration determination in Chinese Pharmacopoeia ) of the assumption of intercept... Of an F-Table - see Appendix 8 depths with the maximum dive times in minutes to obtain best..., mean is not a concern in a simple regression this case the., is used to estimate value of y, 0 ) 24 SSE ) over to.. Your calculator to find a regression line generally goes through the method x... Value of m is a 501 ( c ) ( 3 ) nonprofit,!, on the line and predict the final exam based on the following form: y = 1x ) -3.9057602... ) 24 cm and AC-16 cm then find the least squares regression line b values we were for!

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