Chapter 12: Problem 29
What diagnostic plot can you use to determine whether the incorrect model has been used? What should the plot look like if the correct model has been used?
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Chapter 12: Problem 29
What diagnostic plot can you use to determine whether the incorrect model has been used? What should the plot look like if the correct model has been used?
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You can refresh your memory about regression lines and the correlation coefficient by doing the MyApplet Exercises at the end of Chapter \(3 .\) a. Graph the line corresponding to the equation \(y=0.5 x+3\) by graphing the points corresponding to \(x=0,1,\) and 2 . Give the \(y\) -intercept and slope for the line. b. Check your graph using the How a Line Works applet.
Does a team's batting average depend in any way on the number of home runs hit by the team? The data in the table show the number of team home runs and the overall team batting average for eight selected major league teams for the 2006 season. \(^{14}\) $$ \begin{array}{lcc} \text { Team } & \text { Total Home Runs } & \text { Team Batting Average } \\\ \hline \text { Atlanta Braves } & 222 & .270 \\ \text { Baltimore Orioles } & 164 & .227 \\ \text { Boston Red Sox } & 192 & .269 \\ \text { Chicago White Sox } & 236 & .280 \\ \text { Houston Astros } & 174 & .255 \\ \text { Philadelphia Phillies } & 216 & .267 \\ \text { New York Giants } & 163 & .259 \\ \text { Seattle Mariners } & 172 & .272 \end{array} $$ a. Plot the points using a scatterplot. Does it appear that there is any relationship between total home runs and team batting average? b. Is there a significant positive correlation between total home runs and team batting average? Test at the \(5 \%\) level of significance. c. Do you think that the relationship between these two variables would be different if we had looked at the entire set of major league franchises?
In addition to increasingly large bounds on error, why should an experimenter refrain from predicting \(y\) for values of \(x\) outside the experimental region?
In Exercise 12.15 (data set EX1215), we measured the armspan and height of eight people with the following results: $$ \begin{array}{l|clll} \text { Person } & 1 & 2 & 3 & 4 \\ \hline \begin{array}{l} \text { Armspan (inches) } \\ \text { Height (inches) } \end{array} & 68 & 62.25 & 65 & 69.5 \\ & 69 & 62 & 65 & 70 \\ \text { Person } & 5 & 6 & 7 & 8 \\ \hline \text { Armspan (inches) } & 68 & 69 & 62 & 60.25 \\ \text { Height (inches) } & 67 & 67 & 63 & 62 \end{array} $$ a. Does the data provide sufficient evidence to indicate that there is a linear relationship between armspan and height? Test at the \(5 \%\) level of significance. b. Construct a \(95 \%\) confidence interval for the slope of the line of means, \(\beta\). c. If Leonardo da Vinci is correct, and a person's armspan is roughly the same as the person's height, the slope of the regression line is approximately equal to \(1 .\) Is this supposition confirmed by the confidence interval constructed in part b? Explain.
You are given these data: $$ \begin{array}{l|lllllll} x & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline y & 7 & 5 & 5 & 3 & 2 & 0 \end{array} $$ a. Plot the six points on graph paper. b. Calculate the sample coefficient of correlation \(r\) and interpret. c. By what percentage was the sum of squares of deviations reduced by using the least-squares predictor \(\hat{y}=a+b x\) rather than \(\bar{y}\) as a predictor of \(y ?\)
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