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

$$\begin{matrix} x_i & \text{3} & \text{12} & \text{6} & \text{20} & \text{14}\\ \hline y_i & \text{55} & \text{40} & \text{55} & \text{10} & \text{15}\\ \end{matrix}$$

Develop a scatter diagram for these data.

Use the following data:

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

The estimated regression equation for these data is $\hat { y } = .20 + 2.60 x .$

Compute SSE, SST, and SSR using equations $( 14.8 ) , ( 14.9 ) ,$ and $( 14.10 )$ .

Five observations taken for two variables follow.

$$\begin{matrix} x_i & \text{6} & \text{11} & \text{15} & \text{21} & \text{27}\\ y_i & \text{6} & \text{9} & \text{6} & \text{17} & \text{12}\\ \end{matrix}$$

Develop a scatter diagram for these data.

Five observations taken for two variables follow.

$$\begin{matrix} x_i & \text{4} & \text{6} & \text{11} & \text{3} & \text{16}\\ y_i & \text{50} & \text{50} & \text{40} & \text{60} & \text{30}\\ \end{matrix}$$

Develop a scatter diagram with x on the horizontal axis.

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

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

Try to approximate the relationship between x and y by drawing a straight line through the data.

Use the following data:

$$\begin{matrix} x_i& \text{3} & \text{12} & \text{6} & \text{20} & \text{14}\\ y_i & \text{55} & \text{40} & \text{55} & \text{10} & \text{15}\\ \end{matrix}$$

Estimate the standard deviation of $\hat { y } _ { \mathrm { p } }$ when $x = 8$ .

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

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

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

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

$$\begin{matrix} x_i & \text{3} & \text{12} & \text{6} & \text{20} & \text{14}\\ \hline y_i & \text{55} & \text{40} & \text{55} & \text{10} & \text{15}\\ \end{matrix}$$

Use the estimated regression equation to predict the value of y when x = 10.

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 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.

Five observations taken for two variables follow.

What does the scatter chart developed in part a indicate about the relationship between the two variables?

Use the following data:

$$\begin{matrix} x_i& \text{3} & \text{12} & \text{6} & \text{20} & \text{14}\\ y_i & \text{55} & \text{40} & \text{55} & \text{10} & \text{15}\\ \end{matrix}$$

The estimated regression equation for these data is $\hat { y } = 68 - 3 x .$

Compute SSE, SST, and SSR.

The data from exercise mentioned follow.

a. Compute the mean square error using equation (14.15).

b. Compute the standard error of the estimate using equation (14.16).

c. Compute the estimated standard deviation of $b_1$ using equation (14.18).

d. Use the t test to test the following hypotheses $(\alpha=.05)$ :

$$\begin{aligned} & H_0: \beta_1=0 \\ & H_{\mathrm{a}}: \beta_1 \neq 0 \end{aligned}$$

e. Use the F test to test the hypotheses in part (d) at a .05 level of significance. Present the results in the analysis of variance table format.

Use the following data:

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

Compute the mean square error.