91Ó°ÊÓ

Use the computer output (from different computer packages) to estimate the intercept \(\beta_{0},\) the slope \(\beta_{1},\) and to give the equation for the least squares line for the sample. Assume the response variable is \(Y\) in each case. $$ \begin{array}{lrrrr} \text { Coefficients: } & \text { Estimate } & \text { Std.Error } & \mathrm{t} \text { value } & \mathrm{Pr}(>|\mathrm{t}|) \\ \text { (Intercept) } & 7.277 & 1.167 & 6.24 & 0.000 \\ \text { Dose } & -0.3560 & 0.2007 & -1.77 & 0.087 \end{array} $$

We show an ANOVA table for regression. State the hypotheses of the test, give the F-statistic and the p-value, and state the conclusion of the test. $$ \begin{array}{lrrrr} \text { Analysis of Variance } & & & & \\ \text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text { P } \\ \text { Regression } & 1 & 3396.8 & 3396.8 & 21.85 & 0.000 \\ \text { Residual Error } & 174 & 27053.7 & 155.5 & & \\ \text { Total } & 175 & 30450.5 & & & \end{array} $$

Data 9.1 on page 577 introduces the dataset InkjetPrinters, which includes information on all-in-one printers. Two of the variables are Price (the price of the printer in dollars) and CostColor (average cost per page in cents for printing in color). Computer output for predicting the price from the cost of printing in color is shown: $$ \begin{aligned} &\text { The regression equation is Price }=378-18.6 \text { CostColor }\\\ &\begin{array}{lrrrrr} \text { Analysis of Variance } & & & & \\ \text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text { P } \\ \text { Regression } & 1 & 57604 & 57604 & 13.19 & 0.002 \\ \text { Residual Error } & 18 & 78633 & 4369 & & \\ \text { Total } & 19 & 136237 & & & \end{array} \end{aligned} $$ (a) What is the predicted price of a printer that costs 10 cents a page for color printing? (b) According to the model, does it tend to cost more or less (per page) to do color printing on a cheaper printer? (c) Use the information in the ANOVA table to determine the number of printers included in the dataset. (d) Use the information in the ANOVA table to compute and interpret \(R^{2}\). (e) Is the linear model effective at predicting the price of a printer? Use information from the computer output and state the conclusion in context.

We give computer output with two regression intervals and information about the percent of calories eaten during the day. Interpret each of the intervals in the context of this data situation. (a) The \(95 \%\) confidence interval for the mean response (b) The \(95 \%\) prediction interval for the response The intervals given are for mice that eat \(10 \%\) of their calories during the day: DayPci 1.164 \(\begin{array}{rr}95 \% \mathrm{Cl} & 95 \% \mathrm{P} 1 \\\ (-0.013,4.783) & (-2.797,7.568)\end{array}\) 85 10.0 3888 2:

FIBER IN CEREALS AS A PREDICTOR OF CALORIES In Example 9.10 on page \(592,\) we look at a model to predict the number of calories in a cup of breakfast cereal using the number of grams of sugars. In Exercises 9.64 and 9.65 , we give computer output with two regression intervals and information about a specific amount of sugar. Interpret each of the intervals in the context of this data situation. (a) The \(95 \%\) confidence interval for the mean response (b) The \(95 \%\) prediction interval for the response The intervals given are for cereals with 16 grams of sugars: Sugars 95 \(\mathrm{P}\) \(\begin{array}{rrr}\text { rs Fit } & \text { SE Fit } \\\ 6 & 157.88 & 7.10 & \text { (143.3 }\end{array}\) \(95 \% \mathrm{Cl}\) 35,172.42) \(9 \%\) \(\begin{array}{lllll}16 & 15788 & 7.10 & (143.35,172.42) & (101.46\end{array}\) 214.31)

Golf Scores In a professional golf tournament the players participate in four rounds of golf and the player with the lowest score after all four rounds is the champion. How well does a player's performance in the first round of the tournament predict the final score? Table 9.6 shows the first round score and final score for a random sample of 20 golfers who made the cut in a recent Masters tournament. The data are also stored in MastersGolf. Computer output for a regression model to predict the final score from the first-round score is shown. Use values from this output to calculate and interpret the following. Show your work. (a) Find a \(95 \%\) interval to predict the average final score of all golfers whoshoot a 0 on the first round at the Masters. (b) Find a \(95 \%\) interval to predict the final score of a golfer who shoots a -5 in the first round at the Masters. (c) Find a \(95 \%\) interval to predict the average final score of all golfers who shoot a +3 in the first round at the Masters. The regression equation is Final \(=0.162+1.48\) First \(\begin{array}{lrrrr}\text { Predictor } & \text { Coef } & \text { SE Coef } & \text { T } & \text { P } \\ \text { Constant } & 0.1617 & 0.8173 & 0.20 & 0.845 \\ \text { First } & 1.4758 & 0.2618 & 5.64 & 0.000 \\ S=3.59805 & R-S q=63.8 \% & \text { R-Sq }(a d j) & =61.8 \%\end{array}\) Analysis of Variance Source Regression Residual Error Total \(\begin{array}{rrrrr}\text { DF } & \text { SS } & \text { MS } & \text { F } & \text { P } \\ 1 & 411.52 & 411.52 & 31.79 & 0.000 \\ 18 & 233.03 & 12.95 & & \\ 19 & 644.55 & & & \end{array}\)