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 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:

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

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?

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

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.

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 $( 14.10 )$ .

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

The data from exercise mentioned follow.

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

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 $x=20$.

In a regression analysis involving 30 observations, the following estimated regression equation was obtained.

$$\hat{y}=17.6+3.8 x_1-2.3 x_2+7.6 x_3+2.7 x_4$$

Interpret $b_1, b_2, b_3$, and $b_4$ in this estimated regression equation.

Predict $y$ when $x_1=10, x_2=5, x_3=1$, and $x_4=2$.

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?

The data is below:

$$\begin{array}{r|rrrrr} x_i & 2 & 6 & 9 & 13 & 20 \\ \hline y_i & 7 & 18 & 9 & 26 & 23 \end{array}$$

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?

An important application of regression analysis in accounting is in the estimation of cost. By collecting data on volume and cost and using the least squares method to develop an estimated regression equation relating volume and cost, an accountant can estimate the cost associated with a particular manufacturing volume. Consider the following sample of production volumes and total cost data for a manufacturing operation.

$$\begin{matrix} \text{Production Volume (units)} & \text{Total Cost (\$)}\\ \text{400} & \text{4000}\\ \text{450} & \text{5000}\\ \text{550} & \text{5400}\\ \text{600} & \text{5900}\\ \text{700} & \text{6400}\\ \text{750} & \text{7000}\\ \end{matrix}$$

Use these data to develop an estimated regression equation that could be used to predict the total cost for a given production volume.

An important application of regression analysis in accounting is in the estimation of cost. By collecting data on volume and cost and using the least squares method to develop an estimated regression equation relating volume and cost, an accountant can estimate the cost associated with a particular manufacturing volume. Consider the following sample of production volumes and total cost data for a manufacturing operation.

$$\begin{matrix} \text{Production Volume (units)} & \text{Total Cost (\$)}\\ \text{400} & \text{4000}\\ \text{450} & \text{5000}\\ \text{550} & \text{5400}\\ \text{600} & \text{5900}\\ \text{700} & \text{6400}\\ \text{750} & \text{7000}\\ \end{matrix}$$

The company’s production schedule shows 500 units must be produced next month. What is the estimated total cost for this operation?

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=4.