2.17. The equation of line through. (-1,5) making en
intercept -2 on y-axis
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Answer:
y 11.058-0.01466x 11.058-0.01466 Using this equation, we can add the residuals to the original data: nal data: PASTORE Speed 10 20 30 40 50 60 70 80 Fuel 21.0013.00 10.oo 8.00 7.0o 5.90 6.30 6.95 Residual 10.09 2.24-0.62-2.47-3-33-4.28-3.73-2.94 Speed 9o 100 io 120 130 140 150 Fuel 7.57 8.27 9.03 9.87 10.79 11.77 12.83 Residual -2.17-1.32-0.42 0.57 1.64 2.76 3.97 (a) Make a scatterplot of the observations, and draw the regression line on your plot. (b) Would you use the regression line to predict y from x? Explain your answer. (c) Verify the value of the first residual, for x 10. Verify that the residuals have sum zero (up to roundoff error). (d) Make a plot of the residuals against the values of x. Draw a horizontal line at height zero on your plot. How does the pattern of the residuals about this line compare with the pattern of the data points about the regression line in your scatterplot from part (a)? 5-9: (a) Plot is provided following, top. (b) The pattern is curved, so linear regression is not appropriate. (c) For10, y- 11.058-0.01466(10)- 1o.91 11.08-0.01466(10)10.91, so the residual is 21.00 10.91 10.09. The sum of the residuals is -o.o1. (d) The first two and last four residuals are positive, and those in the middle are negative. Plot following, bottom. Consider Problem 5.9 (p. 142) in the textbook out (i) Do part (a) ) in R. Provide the R code and output (pdf file with overlayed/superimposed regression line). (3 points) (i) Verify the given regression equation by hand using the formulas for the intercept a and slope b, but find the quantities , Sz, S, and r using R (because it would take you forever to find these five quantities by hand!). (4 points) (ii) Verify the given regression equation using R. Provide the relevant R code and output. (Indicate on the R output the quantities a and b.) (3 points) (iv) Answer part (b) of the question (explain). (1 point) (v) Do part (c) of the problem as follows. Calculate the first residual el (when a: = 10) by hand. Then verify the values of all residuals in the table using R. (see class notes for the appropriate R command that generates all residuals, i.e., resid)). Also, verify in R that the sum of the residuals is 0 using the R function sum). Provide all relevant R codes and output. (3 points) (vi) Do part (d) of the problem as follows. Using the statistical package R, plot the residuals (that you obtain using resid)) against the corresponding a-values. The r-values must be on the horizontal axis. Put appropriate labels on the axes and a title on the plot. To get the horizontal line at height zero, we use the R command abline) as follows plot(....) abline(h-0) The letter h means "horizontal".)