Given are data for two variables, x and y.

$$\begin{matrix} x_i & \text{6} & \text{11} & \text{15} & \text{18} & \text{20}\\ y_i & \text{6} & \text{8} & \text{12} & \text{20} & \text{30}\\ \end{matrix}$$

Develop an estimated regression equation for these data.

Consider the following data for two variables, x and y.

$$\begin{matrix} \text{ } & \text{4} & \text{5} & \text{7} & \text{8} & \text{10} & \text{12} & \text{12} & \text{22}\\ \text{ } & \text{12} & \text{14} & \text{16} & \text{15} & \text{18} & \text{20} & \text{24} & \text{19}\\ \end{matrix}$$

a. Compute the standardized residuals for these data. Do the data include any outliers? Explain. b. Compute the leverage values for these data. Do there appear to be any influential observations in these data? Explain. c. Develop a scatter diagram for these data. Does the scatter diagram indicate any influential observations? Explain.

Given are data for two variables, x and y.

$$\begin{matrix} x_i & \text{6} & \text{11} & \text{15} & \text{18} & \text{20}\\ y_i & \text{6} & \text{8} & \text{12} & \text{20} & \text{30}\\ \end{matrix}$$

Develop a plot of the residuals against the independent variable x. Do the assumptions about the error terms seem to be satisfied?

Given are data for two variables, x and y.

$$\begin{array}{c|ccccc} x_i & 6 & 11 & 15 & 18 & 20 \\ \hline y_i & 6 & 8 & 12 & 20 & 30 \end{array}$$

d. Compute the standardized residuals.

Given are five observations collected in a regression study on two variables.

$$\begin{matrix} x_i & \text{2} & \text{6} & \text{9} & \text{13} & \text{20}\\ \hline y_i & \text{7} & \text{18} & \text{9} & \text{26} & \text{23}\\ \end{matrix}$$

Develop a scatter diagram for these data.

Concur Technologies, Inc., is a large expense-management company located in Redmond, Washington. The Wall Street Journal asked Concur to examine the data from 8.3 million expense reports to provide insights regarding business travel expenses. Their analysis of the data showed that New York was the most expensive city, with an average daily hotel room rate of $198 and an average amount spent on entertainment, including group meals and tickets for shows, sports, and other events, of$172. In comparison, the U.S. averages for these two categories were $89 for the room rate and$99 for entertainment. The following table shows the average daily hotel room rate and the amount spent on entertainment for a random sample of 9 of the 25 most visited U.S. cities (The Wall Street Journal, August 18, 2011).

a. Develop a scatter diagram for these data with the room rate as the independent variable.

b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?

c. Develop the least squares estimated regression equation.

d. Provide an interpretation for the slope of the estimated regression equation.

e. The average room rate in Chicago is $\$128$, considerably higher than the U.S. average. Predict the entertainment expense per day for Chicago.

Consider the following data for two variables, x and y.

$$\begin{matrix} x& \text{9} & \text{32} & \text{18} & \text{15} & \text{26}\\ y& \text{10} & \text{20} & \text{21} & \text{16} & \text{22}\\ \end{matrix}$$

a. Develop an estimated regression equation for the data of the form $\hat { y } = b _ { 0 } + b _ { 1 } x$ . Comment on the adequacy of this equation for predicting $y .$ Develop an estimated regression equation for the data of the form $\hat { y } = b _ { 0 } + b _ { 1 } x +$ $b _ { 2 } x ^ { 2 }$ . Comment on the adequacy of this equation for predicting $y .$ c. Predict the value of $y$ when $x = 20$ .

Given are five observations collected in a regression study on two variables.

$$\begin{matrix} x_i & \text{2} & \text{6} & \text{9} & \text{13} & \text{20}\\ \hline y_i & \text{7} & \text{18} & \text{9} & \text{26} & \text{23}\\ \end{matrix}$$

Develop the estimated regression equation for these data.

Given are five observations collected in a regression study on two variables.

$$\begin{matrix} x_i & \text{2} & \text{6} & \text{9} & \text{13} & \text{20}\\ \hline y_i & \text{7} & \text{18} & \text{9} & \text{26} & \text{23}\\ \end{matrix}$$

Use the estimated regression equation to predict the value of y when x = 6.

Given are five observations for two variables, x and y.

$$\begin{matrix} x_i & \text{1} & \text{2} & \text{3} & \text{4} & \text{5}\\ \hline y_i & \text{3} & \text{7} & \text{5} & \text{11} & \text{14}\\ \end{matrix}$$

Develop a scatter diagram for these data.

Following is a portion of the computer output for a regression analysis relating y  maintenance expense (dollars per month) to x = usage (hours per week) of a particular brand of computer terminal.

$$\begin{matrix} \text{The regression equation is}\\ Y=6.1092+.8951X\\\\ \text{Predictor} & \text{Coef} & \text{SE Coef} & \text{Coef}\\ \text{Constant} & \text{6.1092} & \text{0.9361}\\ \text{X} & \text{0.8951} & \text{0.1490}\\\\ \text{Analysis} & \text{of} & \text{Variance}\\\\ \text{SOURCE} & \text{DF} & \text{SS} & \text{MS}\\ \text{Regression} & \text{1} & \text{1575.76} & \text{1575.76}\\ \text{Residual Error} & \text{8} & \text{349.14} & \text{43.64}\\ \text{Total} & \text{9} & \text{1924.90}\\ \end{matrix}$$

a. Write the estimated regression equation. b. Use a t test to determine whether monthly maintenance expense is related to usage at the .05 level of significance. c. Use the estimated regression equation to predict monthly maintenance expense for any terminal that is used 25 hours per week.

Use the following data:

$$\begin{matrix} x_i& \text{2} & \text{6} & \text{9} & \text{13} & \text{20}\\ y_i & \text{7} & \text{18} & \text{9} & \text{26} & \text{23}\\ \end{matrix}$$

What is the value of the standard error of the estimate?

In exercise 20, data on $x$ = weight (pounds) and $y$ = price ($) for 10 road-racing bikes provided the estimated regression equation$^{y}$= 28,574 - 1439$x$. (Bicycling website, March 8, 2012). For these data SSE = 7,102,922.54 and SST = 52,120,800. Use the$F$ test to determine whether the weight of a bike and the price are related at the .05 level of significance.

Consider the following data for two variables, $x$ and $y$.

$$\begin{array}{r|rrrrr} x & 9 & 32 & 18 & 15 & 26 \\ \hline y & 10 & 20 & 21 & 16 & 22 \end{array}$$

a. Develop an estimated regression equation for the data of the form $\hat{y}=b_0+b_1 x$. Comment on the adequacy of this equation for predicting $y$.

b. Develop an estimated regression equation for the data of the form $\hat{y}=b_0+b_1 x+$ $b_2 x^2$. Comment on the adequacy of this equation for predicting $y$.

c. Predict the value of $y$ when $x=20$.