# Complete the estimated regression equation (to 3 decimals). ŷ =  +  x  b.    Compute the residuals (to 2 decimals).

1. Given are the data for two variables, x and y.

 xi 8 13 17 20 22 yi 4 6 10 18 28

a.     Compute b1 and b0 (to 3 decimals).

b1
b0

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Complete the estimated regression equation (to 3 decimals).
ŷ =  +  x

b.    Compute the residuals (to 2 decimals).

 x1 x2 x3 x4 x5

c.

d.    Consider the following three scatter diagrams of the residuals against the independent variable. Which of the following accurately represents the data?

1)

2)

3)

Select Scatter diagram #1 Scatter diagram #2 Scatter diagram #3 Item 10

Do the assumptions about the error terms seem to be satisfied?
Select Yes, the plot of the residuals suggests that the error term assumptions are satisfied No, the plot of the residuals suggests that the error term assumptions are not satisfied Item 11

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2.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.

 Production Volume (units) Total Cost (\$) 400 4,300 450 5,300 550 5,700 600 6,200 700 6,700 750 7,300

a.     Compute b1 and b0 (to 1 decimal).
b1
b0

Complete the estimated regression equation (to 1 decimal).
ŷ =  +  x

b.    What is the variable cost per unit produced (to 1 decimal)?
c.     Compute the coefficient of determination (to 3 decimals). Note: report r2 between 0 and 1.
r2 =

What percentage of the variation in total cost can be explained by the production volume (to 1 decimal)?
%

d.    The company’s production schedule shows 500 units must be produced next month. What is the estimated total cost for this operation (to the nearest whole number)?
\$

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3. The commercial division of a real estate firm is conducting a regression analysis of the relationship between x, annual gross rents (in thousands of dollars), and y, selling price (in thousands of dollars) for apartment buildings. Data were collected on several properties recently sold and the following computer output was obtained.

 The regression equation is Y =20.0 + 7.27 X Predictor Coef SE Coef T Constant 20.000 3.2213 6.21 X 7.270 1.3624 5.29 Analysis of Variance SOURCE DF SS Regression 1 41,587.4 Residual Error 7 Total 8 51,984.3

a.  How many apartment buildings were in the sample?

b.  Write the estimated regression equation (to 2 decimals if necessary).
ŷ =  +  x

c.  What is the value of sb1 (to 4 decimals)?

d.  Use the F statistic to test the significance of the relationship at a .05 level of significance.

Compute the F test statistic (to 2 decimals).

What is the p-value?
p-value is  Select less than .01 between .01 and .025 between .025 and .05 between .05 and .10 greater than .10 Item 6

Select Conclude that the selling price is related to annual gross rents. Cannot conclude that the selling price is related to annual gross rents. Item 7

e. Predict the selling price of an apartment building with gross annual rents of \$60,000 (to 1 decimal).
\$ thousands.

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 4. In exercise 5, the following data on x = the number of defective parts found and y = the line speed (feet per minute) for a production process at Brawdy Plastics provided the estimated regression equation  = 27.5 – .3x. Excel File: data12-37.xls For these data SSE = 16. Develop a 95% confidence interval for the mean number of defective parts for a line speed of 25 feet per minute (to 4 decimals). to

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

 xi 1 2 3 4 5 yi 4 5 8 9 13

a.     Which of the following scatter diagrams accurately represents the data?

1.

2.

3.

Select Scatter diagram #1 Scatter diagram #2 Scatter diagram #3 Item 1

b.    What does the scatter diagram indicate about the relationship between the two variables?
Select There appears to be a linear relationship between x and y There appears to be a nonlinear relationship between x and y Item 2

c.     Develop the estimated regression equation by computing the the slope and the y intercept of the estimated regression line (to 1 decimal).
ŷ =  +  x

d.    Use the estimated regression equation to predict the value of y when x = 4 (to 1 decimal).
ŷ =

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