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

$\boldsymbol{x}_i$	2	6	9	13	20
$\boldsymbol{y}_i$	7	18	9	26	23

a. Develop a scatter diagram for these data.

b. Develop the estimated regression equation for these data.

c. 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.

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

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

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

a. Develop a scatter diagram for these data.

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

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

d. Develop the estimated regression equation by computing the values of $b_0$ and $b_1$ using equations mentioned.

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

Use these data to develop an estimated regression equation that could be used to predict the average annual salary for salaried employees given the average annual salary for hourly employees.

Use the data to develop an estimated regression equation that could be used to estimate the price for a bike given the weight.

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.

Use the following data:

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

The estimated regression equation for these data is $\hat { y } = 7.6 + .9 x .$ What percentage of the total sum of squares can be accounted for by the estimated regression equation? What is the value of the sample correlation coefficient?

The data from exercise mentioned follow.

Develop the 95% confidence and prediction intervals when x=12. Explain why these two intervals are different.

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 the estimated regression equation by computing the values of b0 and b1 using equations.

Brawdy Plastics, Inc., produces plastic seat belt retainers for General Motors at the Brawdy Plastics plant in Buffalo, New York. After final assembly and painting, the parts are placed on a conveyor belt that moves the parts past a final inspection station. How fast the parts move past the final inspection station depends upon the line speed of the conveyor belt (feet per minute). Although faster line speeds are desirable, management is concerned that increasing the line speed too much may not provide enough time for inspectors to identify which parts are actually defective. To test this theory, Brawdy Plastics conducted an experiment in which the same batch of parts, with a known number of defective parts, was inspected using a variety of line speeds. The following data were collected.

$$\begin{array}{cc}\text { Line } & \begin{array}{c}\text { Number of } \\ \text { Speed } \\ \text { Defective } \\ \text { Parts Found }\end{array} \\ 20 & 23 \\ 20 & 21 \\ 30 & 19 \\ 30 & 16 \\ 40 & 15 \\ 40 & 17 \\ 50 & 14 \\ 50 & 11\end{array}$$

Predict the number of defective parts found for a line speed of 25 feet per minute.

Five observations taken for two variables follow.

Compute and interpret the sample covariance.

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

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

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

Five observations taken for two variables follow.

Compute and interpret the sample correlation coefficient.

A large city hospital conducted a study to investigate the relationship between the number of unauthorized days that employees are absent per year and the distance (miles) between home and work for the employees. A sample of 10 employees was selected and the following data were collected.

$$\begin{array}{cc}\text{Distance to Work} & \text{Number of Days}\\\text { (miles) } & \text { Absent } \\ 1 & 8 \\ 3 & 5 \\ 4 & 8 \\ 6 & 7 \\ 8 & 6 \\ 10 & 3 \\ 12 & 5 \\ 14 & 2 \\ 14 & 4 \\ 18 & 2\end{array}$$

a. Develop a scatter diagram for these data. Does a linear relationship appear reasonable? Explain.

b. Develop the least squares estimated regression equation that relates the distance to work to the number of days absent.

c. Predict the number of days absent for an employee that lives 5 miles from the hospital.