The following data represent the number of calories per serving and the number of grams of sugar per serving for a random sample of high-protein and moderate-protein energy bars.
$$\begin{array}{cc|cc}
\text { Calories, } \boldsymbol{x} & \text { Sugar, } \boldsymbol{y} & \text { Calories, } \boldsymbol{x} & \text { Sugar, } \boldsymbol{y} \\
\hline 180 & 10 & 270 & 20 \\
\hline 200 & 18 & 320 & 2 \\
\hline 210 & 14 & 110 & 10 \\
\hline 220 & 20 & 180 & 12 \\
\hline 220 & 0 & 200 & 22 \\
\hline 230 & 28 & 220 & 24 \\
\hline 240 & 2 & 230 & 24 \\
\hline \text { Source: Consumer Reports } & &
\end{array}$$
(a) Draw a scatter diagram of the data, treating calorics as the explanatory variable. What type of relation, if any, appears to exist between calories and sugar?
(b) Determine the least-squares regression equation from the sample data.
(c) Compute the standard error of the estimate.
(d) Determine whether the residuals are normally distributed.
(e) Determine $s_{b}$
(f) If the residuals are normally distributed, test whether a linear relation exists between calories and sugar content at the $\alpha=0.01$ level of significance.
(g) If the residuals are normally distributed, construct a $95 \%$ confidence interval about the slope of the true least-squares regression line.
(h) For a randomly selected energy bar, would you recommend using the least-squares regression line obtained in part (b) to predict the sugar content of the energy bar? Why? What would be a good estimate for the sugar content of the encrgy bar?