Commercial contractors and home improvement merchants like Lowe's and Home Depot can purchase roofing and siding supplies from Great Plains Distributors Inc. The business owner is curious to know how different factors affect how much fiber-cement siding is sold. In the United States, the corporation operates 26 marketing districts. It gathered data on the following factors in each district: sales volume (in thousands of dollars), advertising spending (in thousands of dollars), the number of active accounts, the number of rival brands, and an assessment of market potential.

$$\begin{array}{|ccccc|} \begin{array}{c} \text { Sales } \\ \text { (000s) } \end{array} & \begin{array}{c} \text { Advertising } \\ \text { Dollars } \\ \text { (000s) } \end{array} & \begin{array}{c} \text { Number of } \\ \text { Accounts } \end{array} & \begin{array}{c} \text { Number of } \\ \text { Competitors } \end{array} & \begin{array}{c} \text { Market } \\ \text { Potential } \end{array} \\ \hline 79.3 & 5.5 & 31 & 10 & 8 \\ 200.1 & 2.5 & 55 & 8 & 6 \\ 163.2 & 8.0 & 67 & 12 & 9 \\ 200.1 & 3.0 & 50 & 7 & 16 \\ 146.0 & 3.0 & 38 & 8 & 15 \\ 177.7 & 2.9 & 71 & 12 & 17 \\ \vdots & \vdots & \vdots & & \\ 93.5 & 4.2 & 26 & 8 & 3 \\ 259.0 & 4.5 & 75 & 4 & 9 \\ 331.2 & 5.6 & 71 & & \\ \hline \end{array}$$

Find the most accurate sales predictors by performing a multivariate regression analysis. Using this, develop a histogram of the residuals and a normal probability plot. Are there any problems?

Solve for $x$ by writing the equation in exponential form.

$$\log _4 x=-2$$

Commercial contractors and home improvement merchants like Lowe's and Home Depot can purchase roofing and siding supplies from Great Plains Distributors Inc. The business owner is curious to know how different factors affect how much fiber-cement siding is sold. In the United States, the corporation operates 26 marketing districts. It gathered data on the following factors in each district: sales volume (in thousands of dollars), advertising spending (in thousands of dollars), the number of active accounts, the number of rival brands, and an assessment of market potential.

$$\begin{array}{|ccccc|} \begin{array}{c} \text { Sales } \\ \text { (000s) } \end{array} & \begin{array}{c} \text { Advertising } \\ \text { Dollars } \\ \text { (000s) } \end{array} & \begin{array}{c} \text { Number of } \\ \text { Accounts } \end{array} & \begin{array}{c} \text { Number of } \\ \text { Competitors } \end{array} & \begin{array}{c} \text { Market } \\ \text { Potential } \end{array} \\ \hline 79.3 & 5.5 & 31 & 10 & 8 \\ 200.1 & 2.5 & 55 & 8 & 6 \\ 163.2 & 8.0 & 67 & 12 & 9 \\ 200.1 & 3.0 & 50 & 7 & 16 \\ 146.0 & 3.0 & 38 & 8 & 15 \\ 177.7 & 2.9 & 71 & 12 & 17 \\ \vdots & \vdots & \vdots & & \\ 93.5 & 4.2 & 26 & 8 & 3 \\ 259.0 & 4.5 & 75 & 4 & 9 \\ 331.2 & 5.6 & 71 & & \\ \hline \end{array}$$

Find the most accurate sales predictors by performing a multivariate regression analysis. Using this, develop a regression equation. Conduct the global test. Can we conclude that some of the independent variables are useful in explaining the variation in the dependent variable?

Commercial contractors and home improvement merchants like Lowe's and Home Depot can purchase roofing and siding supplies from Great Plains Distributors Inc. The business owner is curious to know how different factors affect how much fiber-cement siding is sold. In the United States, the corporation operates 26 marketing districts. It gathered data on the following factors in each district: sales volume (in thousands of dollars), advertising spending (in thousands of dollars), the number of active accounts, the number of rival brands, and an assessment of market potential.

$$\begin{array}{|ccccc|} \begin{array}{c} \text { Sales } \\ \text { (000s) } \end{array} & \begin{array}{c} \text { Advertising } \\ \text { Dollars } \\ \text { (000s) } \end{array} & \begin{array}{c} \text { Number of } \\ \text { Accounts } \end{array} & \begin{array}{c} \text { Number of } \\ \text { Competitors } \end{array} & \begin{array}{c} \text { Market } \\ \text { Potential } \end{array} \\ \hline 79.3 & 5.5 & 31 & 10 & 8 \\ 200.1 & 2.5 & 55 & 8 & 6 \\ 163.2 & 8.0 & 67 & 12 & 9 \\ 200.1 & 3.0 & 50 & 7 & 16 \\ 146.0 & 3.0 & 38 & 8 & 15 \\ 177.7 & 2.9 & 71 & 12 & 17 \\ \vdots & \vdots & \vdots & & \\ 93.5 & 4.2 & 26 & 8 & 3 \\ 259.0 & 4.5 & 75 & 4 & 9 \\ 331.2 & 5.6 & 71 & & \\ \hline \end{array}$$

Find the most accurate sales predictors by performing a multivariate regression analysis. Using this, draw a scatter diagram comparing sales volume with each of the independent variables. Comment on the results.

Commercial contractors and home improvement merchants like Lowe's and Home Depot can purchase roofing and siding supplies from Great Plains Distributors Inc. The business owner is curious to know how different factors affect how much fiber-cement siding is sold. In the United States, the corporation operates 26 marketing districts. It gathered data on the following factors in each district: sales volume (in thousands of dollars), advertising spending (in thousands of dollars), the number of active accounts, the number of rival brands, and an assessment of market potential.

$$\begin{array}{|ccccc|} \begin{array}{c} \text { Sales } \\ \text { (000s) } \end{array} & \begin{array}{c} \text { Advertising } \\ \text { Dollars } \\ \text { (000s) } \end{array} & \begin{array}{c} \text { Number of } \\ \text { Accounts } \end{array} & \begin{array}{c} \text { Number of } \\ \text { Competitors } \end{array} & \begin{array}{c} \text { Market } \\ \text { Potential } \end{array} \\ \hline 79.3 & 5.5 & 31 & 10 & 8 \\ 200.1 & 2.5 & 55 & 8 & 6 \\ 163.2 & 8.0 & 67 & 12 & 9 \\ 200.1 & 3.0 & 50 & 7 & 16 \\ 146.0 & 3.0 & 38 & 8 & 15 \\ 177.7 & 2.9 & 71 & 12 & 17 \\ \vdots & \vdots & \vdots & & \\ 93.5 & 4.2 & 26 & 8 & 3 \\ 259.0 & 4.5 & 75 & 4 & 9 \\ 331.2 & 5.6 & 71 & & \\ \hline \end{array}$$

Find the most accurate sales predictors by performing a multivariate regression analysis. Using this, develop a correlation matrix. Do you see any problems? Does it appear there are any redundant independent variables?

Following are two income statements for Alexis Co. for the year ended December 31. The left number column is prepared before any adjusting entries are recorded, and the right column includes the effects of adjusting entries. The middle column shows a blank space for each income statement effect of the eight adjusting entries a through g (the balance sheet part of the entries is not shown here). Analyze the statements and prepare the eight adjusting entries a through g that likely were recorded. Note: Answer for a has two entries (i) of the $7,000 adjustment for Fees Earned, 30% (or$2,100) has been earned but not billed, and (ii) the other 70% (or $4,900) has been earned by performing services that were paid for in advance.$

$$\begin{matrix} \text{ALEXIS CO. Income Statements For Year Ended December 31}\\ & \text{Unadjusted} & \text{Adjustments} & \text{Adjusted}\\ \text{Revenues }\\ \text{Fees earned} \ldots\ldots\ldots & \text{\$18,000} & \text{a} & \text{\$25,000}\\ \text{Commissions earned} \ldots\ldots\ldots & \text{36,500} & \quad & \text{36,500}\\ \text{Total revenues} \ldots\ldots\ldots & \text{54,500} & \quad & \text{61,500}\\ \text{Expenses} \ldots\ldots\ldots \\ \text{Depreciation expense—Computers} \ldots\ldots\ldots & \text{0} & \text{b} & \text{1,600}\\ \text{Depreciation expense—Office furniture} \ldots\ldots\ldots & \text{0} & \text{c} & \text{1,850}\\ \text{Salaries expense} \ldots\ldots\ldots & \text{13,500} & \text{d} & \text{15,750}\\ \text{Insurance expense} \ldots\ldots\ldots & \text{0} & \text{e} & \text{1,400}\\ \text{Rent expense} \ldots\ldots\ldots & \text{3,800} & \quad & \text{3,800}\\ \text{Office supplies expense} \ldots\ldots\ldots & \text{0} & \text{f} & \text{580}\\ \text{Advertising expense} \ldots\ldots\ldots & \text{2,500} & \quad & \text{2,500}\\ \text{Utilities expense} \ldots\ldots\ldots & \text{1,245} & \text{f} & \text{1,335}\\ \text{Total expenses} \ldots\ldots\ldots & \text{21,045} & \quad & \text{28,815}\\ \text{Net income} \ldots\ldots\ldots & \text{\$33,455} & \quad & \text{\$32,685}\\ \end{matrix}$$

$

The demographics of nine counties in an Atlantic seaboard state's eastern section are being researched by a regional planner. She's compiled the following information:

$$\begin{array}{|cccc|} \hline \text { County } & \text { Median Income } & \text { Median Age } & \text { Coastal}^* \\ \hline \text { A } & \$ 48,157 & 57.7 & 1 \\ \text { B } & 48,568 & 60.7 & 1 \\ \text { C } & 46,816 & 47.9 & 1 \\ \text { D } & 34,876 & 38.4 & 0 \\ \text { E } & 35,478 & 42.8 & 0 \\ \text { F } & 34,465 & 35.4 & 0 \\ \text { G } & 35,026 & 39.5 & 0 \\ \text { H } & 38,599 & 65.6 & 0 \\ \text { J } & 33,315 & 27.0 & 0 \\ { }^* 1=\text { yes, } 0=\text { no. } & & & \\ \hline \end{array}$$

Using this, test each of the individual coefficients to see if they are significant.

Consider the ANOVA table that follows. Analysis of Variance

$$\begin{array}{lrrrr}\text { Source } & \text { DF } & \text { SS } & \text { MS } & F \\ \text { Regression } & 5 & 3710.00 & 742.00 & 12.89 \\ \text { Residual Error } & 46 & 2647.38 & 57.55 & \\ \text { Total } & 51 & 6357.38 & & \end{array}$$

a. Determine the standard error of estimate. About $95 \%$ of the residuals will be between what two values? b. Determine the coefficient of multiple determination. Interpret this value. c. Determine the coefficient of multiple determination, adjusted for the degrees of freedom.

A sample of General Mills employees was studied to determine their degree of satisfaction with their quality of life. A special index, called the index of satisfaction, was used to measure satisfaction. Six factors were studied, namely, age at the time of first marriage

$$(X_1)$$

, annual income

$$(X_2)$$

, number of children living

$$(X_3)$$

, value of all assets

$$(X_4)$$

, status of health in the form of an index

$$(X_5)$$

, and the average number of social activities per week—such as bowling and dancing

$$(X_6).$$

Suppose the multiple regression equation is: Ŷ=

$$16.24 + 0.017X_1 + 0.0028X_2 + 42X_3 + 0.0012X_4 + 0.19X_5 + 26.8X_6$$

a. What is the estimated index of satisfaction for a person who first married at 18, has an annual income of $26,500, has three children living, has assets of$156,000, has an index of health status of 141, and has 2.5 social activities a week on the average? b. Which would add more to satisfaction, an additional income of $10,000 a year or two more social activities a week?

Using Exercise 16, determine the .95 prediction interval, in thousands of dollars, for a particular salesperson who makes 40 contacts.

On the first statistics exam, the coefficient of determination between the hours studied and the grade earned was $80 \%$. The standard error of estimate was 10 . There were 20 students in the class. Develop an ANOVA table for the regression analysis of hours studied as a predictor of the grade earned on the first statistics exam.

Refer to Exercise . The regression equation is $\hat{y}=29.29-0.96 x$, the sample size is 8 , and the standard error of the slope is 0.22 . Use the .05 significance level. Can we conclude that the slope of the regression line is less than zero?

The owner of Maumee Ford-Volvo wants to study the relationship between the age of a car and its selling price. Listed is a random sample of 12 used cars sold at the dealership during the last year.

$$\begin{array}{|cccccc|} \hline \text { Car } & \text { Age (years) } & \text { Selling Price }(\$ 000) & \text { Car } & \text { Age (years) } & \text { Selling Price }(\$ 000) \\ 1 & 9 & 8.1 & 7 & 8 & 7.6 \\ 2 & 7 & 6.0 & 8 & 11 & 8.0 \\ 3 & 11 & 3.6 & 9 & 10 & 8.0 \\ 4 & 12 & 4.0 & 10 & 12 & 6.0 \\ 5 & 8 & 5.0 & 11 & 6 & 8.6 \\ 6 & 7 & 10.0 & 12 & 6 & 8.0 \\ \hline \end{array}$$

a. Draw a scatter diagram. b. Determine the correlation coefficient. c. Interpret the correlation coefficient. Does it surprise you that the correlation coefficient is negative?

We are studying mutual bond funds for the purpose of investing in several funds. For this particular study, we want to focus on the assets of a fund and its 5-year performance. The question is: Can the 5-year rate of return be estimated based on the assets of the fund? Nine mutual funds were selected at random, and their assets and rates of return are as follows:

$$\begin{array}{|c|c|c|c|c|c|} \hline \text { Fund } & \begin{array}{l} \text { Assets } \\ \text{ (\$ millions) } \end{array} & \begin{array}{l} \text { Return } \\ \text{ (\\\%) } \end{array} & \text { Fund } & \begin{array}{c} \text { Assets } \\ \text{ (\$ millions) } \end{array} & \begin{array}{l} \text { Return } \\ (\%) \end{array} \\ \hline \text { AARP High Quality Bond } & \$ 622.2 & 10.8 & \text { MFS Bond A } & \$ 494.5 & 11.6 \\ \hline \text { Babson Bond L } & 160.4 & 11.3 & \text { Nichols Income } & 158.3 & 9.5 \\ \hline \text { Compass Capital Fixed Income } & 275.7 & 11.4 & \text { T. Rowe Price Short-term } & 681.0 & 8.2 \\ \hline \text { Galaxy Bond Retail } & 433.2 & 9.1 & \text { Thompson Income B } & 241.3 & 6.8 \\ \hline \text { Keystone Custodian B-1 } & 437.9 & 9.2 & & & \\ \hline \end{array}$$