Chapter 8 Regression Analysis

In a simple linear regression equation where advertising expenditures is used to predict sales, which of the following is true?

Advertising expenditures is the independent variable and sales is the dependent variable.

How does a multiple linear regression equation differ from a simple linear regression equation?

More than one independent variable is used to predict a dependent variable in a multiple linear regression equation but only one independent variable is used to predict a dependent variable in a simple linear regression equation.

High Concept Fashion is planning its next advertising campaign to coincide with its store expansion in the following months. Using information from the past few years, the company was able to perform a regression analysis with the following results: Sales revenue = $200,000 + 15(Advertising budget) R2 = 0.85 The company's advertising budget over the last few years usually fell between the range of $10,000 and $15,000 a year. It plans on spending $50,000 this year as a result of its expansion. Given its new advertising budget, High Concept Fashion should expect:

Unable to make any prediction because the new budget lies outside the range of the sample used to estimate the regression equation.

In a simple linear regression equation where units produced is used to predict electricity costs, which of the following is true?

Units produced is the independent variable and electricity costs is the dependent variable.

Which of the following concerning simple linear regression analysis is correct?

A higher coefficient of determination (R-squared) is preferred to a lower one since it measures the amount of variability in the dependent variable explained by changes in the independent variable.

Dawson Manufacturing developed the following multiple regression equation, utilizing many years of data, and uses it to model, or estimate, the cost of its product. Cost = FC + a × L + b × M Where: FC = fixed costs L = labor rate per hour M = material cost per pound Which one of the following changes would have the greatest impact on invalidating the results of this model?

A significant change in labor productivity.

Dawson Manufacturing developed the following multiple regression equation, utilizing many years of data, and uses it to model, or estimate, the total cost of its product. Cost = FC + L(A) + M(B) Where: FC = total fixed costs L = labor rate per hour A= number of labor hours in the product M = material cost per pound B = number of machine hours in the product Which one of the following changes would have the greatest impact on invalidating the results of this model?

A significant change in the design of the product

Maxis Tech is trying to determine how an employee's performance rating could be explained by his/her level of education (EDU), the length of employment (EMP) with the company, and the number of training (TRN) hours received. Using data from 100 of its employees, Maxis Tech performs a regression analysis with the following results: Performance rating = 0.2 + 0.32 EDU + 0.15 EMP + 0.07 TRN R2 = 0.72 t for EDU = 0.013 t for EMP = 3.276 t for TRN = 4.121 The value of these terms in the parentheses (EDU, EMP, and TRN) represent the t-statistics of the regression coefficient. Which of the following statements best describes the statistical significance of the impact of the three factors on employee performance ratings?

Both length of employment with the company and number of training hours received have statistically significant impact because the absolute values of their t-statistics are higher than the most extreme cutoff point.

The results of regressing Y against X are as follows. Intercept 5.23 Slope 1.54 When the value of X is 10, the estimated value of Y is:

Given this information, the regression equation would be Y = 5.23 + 1.54X. Therefore, if X = 10, it can be plugged into the equation as follows: Y = 5.23 + 1.54(10) Y = 5.23 + 15.4 = 20.63 20.63

In order to analyze sales as a function of advertising expenses, the sales manager of Smith Company developed a simple regression model. The model included the following equation, which was based on 32 monthly observations of sales and advertising expenses with a related coefficient of determination of 0.90. S = $10,000 + $2.50A S = sales A = advertising expenses If Smith Company's advertising expenses in one month amounted to $1,000, the related point estimate of sales would be:

If advertising expense is $1,000, then $1,000 can be plugged into the regression equation for variable "A" as follows: S = $10,000 + $2.50A S = $10,000 + $2.50($1,000) S = $12,500 12,500

Connor's Shirt Shop performed a regression analysis on its delivery costs for the previous 12 months. The number of deliveries during those 12 months ranged from 10,000 deliveries to 15,000 deliveries. The regression analysis yielded an intercept of $9,000, a coefficient on deliveries of $3.50, and an R-squared of 92.6%. If Connor expects to make 14,000 deliveries in the next month, what would Connor estimate total delivery costs to be?

Regression analysis produces an "intercept" and a "slope coefficient." The "intercept" is the estimate of fixed costs and the "slope coefficient" is the estimate of variable cost per unit of volume. Based on the regression analysis performed, Connor's fixed costs to make 14,000 deliveries are estimated as $9,000 and variable costs to make 14,000 deliveries are estimated as $49,000 ($3.50 × 14,000). This results in a total estimated cost to make 14,000 deliveries of $58,000 ($9,000 + $49,000); therefore, this is the correct answer. 58,000

Sophia Company performed a regression analysis on its customer service costs for the previous 12 months. The number of orders during those 12 months ranged from 5,000 orders to 12,000 orders and the customer service costs ranged from $120,000 to $300,000. The regression analysis yielded an intercept of $30,000, a coefficient on orders of $22, and an R-squared of 91.3%. If Sophia expects to have 9,000 orders in the next month, what would Sophia estimate total customer service costs to be?

Regression analysis produces an "intercept" and a "slope coefficient." The "intercept" is the estimate of fixed costs and the "slope coefficient" is the estimate of variable cost per unit of volume. Based on the regression analysis performed, Sophia's fixed costs for 9,000 orders are estimated as $30,000 and variable costs for 9,000 orders are estimated as $198,000 ($22 × 9,000). This results in a total estimated customer service cost for 9,000 orders of $228,000 ($30,000 + $198,000). Therefore, this is the correct answer. 228,000

Gill's Golf Gear (GGG) conducted a regression analysis on its shipping costs for the last year, which resulted in the following equation: $2.30x + $375. If GGG plans to ship 320 boxes of golf balls next month, what are the shipping costs expected to be?

Regression analysis uses past data to develop an equation that can be used to make predictions about the future. Simple regression involves using one independent variable (for example, sales, production, or some other measure of volume) to predict future costs. Regression analysis produces an "intercept" and a "slope coefficient." The "intercept" is the estimate of fixed costs and the "slope coefficient" is the estimate of variable cost per unit of volume. Based on the regression analysis performed, GGG's fixed costs for 320 shipments are estimated as $375 and variable costs for 320 shipments are estimated as $736 ($2.30 × 320). This results in a total estimated cost for 320 shipments of $1,111.00 ($736 + $375); therefore, this is the correct answer. 1,111.00

Eight quarters of production data from Pear, Inc., a cell phone manufacturing company, are below. Quarter Phones Shut Downs Costs 1 -- 2,331 -- 3,245,874 2 -- 2,657 -- 3,474,318 3 -- 1,987 -- 2,883,675 4 -- 2,412 -- 3,287,621 5 -- 2,583 -- 3,354,966 6 --2,497 -- 3,428,752 7 -- 2,285 -- 3,152,347 8 -- 2,645 -- 3,271,899 The regression analysis results on these data are displayed below. Coefficients Standard error Tstat P-value Lovers 95% Upper 95% Intercept 1,473,119--356,978--4.13--.01--599,625--2,346,614 Phones 738--147--5.03--0.00--379--1,097 Regression Statistics Multiple R .90 R Squared .81 Adjusted R squared .78 Standard error 87,127 Observations 8 Which measure from the regression analysis result is the best indicator of how much we understand about total costs in the dataset based on the volume of phone production in the dataset?

The Adjusted R Square is the R Square metric adjusted for the size of the data set. The Adjusted R Square is a more appropriate measure to use when explaining variance in cost data. In this case, the 0.78 statistic means that variance (change) in phone production explains 78% of the variance (change) in costs. Adjusted R Square of 0.78

Eight quarters of production data from Pear, Inc., a cell phone manufacturing company, are below. Quarter Phones Shut Downs Costs 1 -- 2,331 -- 2 -- 3,245,874 2 -- 2,657 -- 1 -- 3,474,318 3 -- 1,987 -- 3 -- 2,883,675 4 -- 2,412 -- 2 -- 3,287,621 5 -- 2,583 -- 1 -- 3,354,966 6 --2,497 -- 3 -- 3,428,752 7 -- 2,285 -- 2 -- 3,152,347 8 -- 2,645 -- 0 -- 3,271,899 The regression analysis results on these data are displayed below. Coefficients Standard error Tstat P-value Lovers 95% Upper 95% Intercept 466,096--309,413--1.51--.19--(329,275)--1,261,467 Phones 1,080--114--9.50--0.00--788-1,373 Shut Downs 100,963--24,675--4.09--.01--37,534--164,931 Regression Statistics Multiple R .98 R Squared .96 Adjusted R squared .94 Standard error 45,769 Observations 8 Evaluate the Multiple R.

The Multiple R statistic of 0.98 is the correlation of total costs, volume of phone production, and number of shutdowns. There is a 98% correlation between these numbers.

Which of the following correctly describes the use of the output from a simple linear regression analysis?

The coefficient of the "intercept" is the estimate of the fixed component of the dependent variable and the coefficient on the independent variable is the estimate of variable amount per unit of the independent variable.

Which of the following concerning simple linear regression analysis is not correct?

The coefficient of the "intercept" resulting from a regression analysis where marketing expenditures ranging from $10,000 per month to $20,000 per month and sales ranging from $250,000 per month to $600,000 per month are used is the estimated sales when marketing expenditures are zero.

Eight quarters of production data from Pear, Inc., a cell phone manufacturing company, are below. Quarter Phones Shut Downs Costs 1 -- 2,331 -- 3,245,874 2 -- 2,657 -- 3,474,318 3 -- 1,987 -- 2,883,675 4 -- 2,412 -- 3,287,621 5 -- 2,583 -- 3,354,966 6 --2,497 -- 3,428,752 7 -- 2,285 -- 3,152,347 8 -- 2,645 -- 3,271,899 The regression analysis results on these data are displayed below. Coefficients Standard error Tstat P-value Lovers 95% Upper 95% Intercept 1,473,119--356,978--4.13--.01--599,625--2,346,614 Phones 738--147--5.03--0.00--379--1,097 Regression Statistics Multiple R .90 R Squared .81 Adjusted R squared .78 Standard error 87,127 Observations 8 Evaluate the estimate for total fixed costs.

The estimate for total fixed costs is acceptably precise for the following reasons: The t-Stat of 4.13 is more than the preferred statistical significance, which traditionally demands a t-Stat of 3 or greater. The P-value of 0.01 is less than the preferred statistical significance, which traditionally demands a P-value of 0.05 or lower.

ABC Company has run a regression analysis and determined that sales are related to marketing costs. The regression formula the analysts have calculated is Y = $5,000,000 + $125(x), where Y = sales and x = marketing costs. Use the regression formula to determine what the annual sales will be if marketing expenditures are $1,000,000.

The regression formula states that: Y = $5,000,000 + $125X where Y = sales and X = marketing costs Y = $5,000,000 + $125($1,000,000) Y = $5,000,000 + $125,000,000 Y = $130,000,000 130,000,000

In order to determine how its in-house training program is affecting its employees' performance rating, Maxis Tech performed a regression analysis with the following results: Performance rating = 0.2 + 0.05 hours of training R2 = 0.1 Given the above information, Maxis Tech can conclude that:

There are factors other than number of training hours received that can better explain an employee's performance rating.

Eight quarters of production data from Pear, Inc., a cell phone manufacturing company, are below. Quarter Phones Shut Downs Costs 1 -- 2,331 -- 3,245,874 2 -- 2,657 -- 3,474,318 3 -- 1,987 -- 2,883,675 4 -- 2,412 -- 3,287,621 5 -- 2,583 -- 3,354,966 6 --2,497 -- 3,428,752 7 -- 2,285 -- 3,152,347 8 -- 2,645 -- 3,271,899 The regression analysis results on these data are displayed below. Coefficients Standard error Tstat P-value Lovers 95% Upper 95% Intercept 1,473,119--356,978--4.13--.01--599,625--2,346,614 Phones 738--147--5.03--0.00--379--1,097 Regression Statistics Multiple R .90 R Squared .81 Adjusted R squared .78 Standard error 87,127 Observations 8 Describe the confidence interval for the variable cost per phone as found in the regression analysis result.

There is a 95% probability that the variable cost per phone is between $379 and $1,097.

Eight quarters of production data from Pear, Inc., a cell phone manufacturing company, are below. Quarter Phones Shut Downs Costs 1 -- 2,331 -- 2 -- 3,245,874 2 -- 2,657 -- 1 -- 3,474,318 3 -- 1,987 -- 3 -- 2,883,675 4 -- 2,412 -- 2 -- 3,287,621 5 -- 2,583 -- 1 -- 3,354,966 6 --2,497 -- 3 -- 3,428,752 7 -- 2,285 -- 2 -- 3,152,347 8 -- 2,645 -- 0 -- 3,271,899 The regression analysis results on these data are displayed below. Coefficients Standard error Tstat P-value Lovers 95% Upper 95% Intercept 466,096--309,413--1.51--.19--(329,275)--1,261,467 Phones 1,080--114--9.50--0.00--788-1,373 Shut Downs 100,963--24,675--4.09--.01--37,534--164,931 Regression Statistics Multiple R .98 R Squared .96 Adjusted R squared .94 Standard error 45,769 Observations 8 Based on the regression analysis result above, and with approximately 68% confidence, predict the total cost to produce 2,500 phones next quarter that includes 2 shutdowns.

This answer calculates the total cost using the regression equation (total cost equation): Total costs = ($1,080 × 2,500 phones) + ($100,963 × 2 shutdowns) + $466,096 = $3,368,022. Then it calculates the 68% confidence interval, which is one standard error: $3,368,022 ± $45,769 = between $3,322,253 and $3,413,791. Between $3,322,253 and $3,413,791

Eight quarters of production data from Pear, Inc., a cell phone manufacturing company, are below. Quarter Phones Shut Downs Costs 1 -- 2,331 -- 3,245,874 2 -- 2,657 -- 3,474,318 3 -- 1,987 -- 2,883,675 4 -- 2,412 -- 3,287,621 5 -- 2,583 -- 3,354,966 6 --2,497 -- 3,428,752 7 -- 2,285 -- 3,152,347 8 -- 2,645 -- 3,271,899 The regression analysis results on these data are displayed below. Coefficients Standard error Tstat P-value Lovers 95% Upper 95% Intercept 1,473,119--356,978--4.13--.01--599,625--2,346,614 Phones 738--147--5.03--0.00--379--1,097 Regression Statistics Multiple R .90 R Squared .81 Adjusted R squared .78 Standard error 87,127 Observations 8 Based on the regression analysis result above, and with approximately 68% confidence, predict the total cost to produce 2,500 phones next quarter.

This answer calculates the total cost using the regression equation (total cost equation): Total costs = ($738 × 2,500 phones) + $1,473,119 = $3,318,119. Then it calculates the 68% confidence interval, which is one standard error: $3,318,119 ± $87,127 = between $3,230,992 and $3,405,246. Between $3,230,992 and $3,405,246

Eight quarters of production data from Pear, Inc., a cell phone manufacturing company, are below. Quarter Phones Shut Downs Costs 1 -- 2,331 -- 3,245,874 2 -- 2,657 -- 3,474,318 3 -- 1,987 -- 2,883,675 4 -- 2,412 -- 3,287,621 5 -- 2,583 -- 3,354,966 6 --2,497 -- 3,428,752 7 -- 2,285 -- 3,152,347 8 -- 2,645 -- 3,271,899 The regression analysis results on these data are displayed below. Coefficients Standard error Tstat P-value Lovers 95% Upper 95% Intercept 1,473,119--356,978--4.13--.01--599,625--2,346,614 Phones 738--147--5.03--0.00--379--1,097 Regression Statistics Multiple R .90 R Squared .81 Adjusted R squared .78 Standard error 87,127 Observations 8 What is the regression equation (total cost equation) for the above information?

Total costs = $738(Phones) + $1,473,119

Eight quarters of production data from Pear, Inc., a cell phone manufacturing company, are below. Quarter Phones Shut Downs Costs 1 -- 2,331 -- 3,245,874 2 -- 2,657 -- 3,474,318 3 -- 1,987 -- 2,883,675 4 -- 2,412 -- 3,287,621 5 -- 2,583 -- 3,354,966 6 --2,497 -- 3,428,752 7 -- 2,285 -- 3,152,347 8 -- 2,645 -- 3,271,899 The regression analysis results on these data are displayed below. Coefficients Standard error Tstat P-value Lovers 95% Upper 95% Intercept 1,473,119--356,978--4.13--.01--599,625--2,346,614 Phones 738--147--5.03--0.00--379--1,097 Regression Statistics Multiple R .90 R Squared .81 Adjusted R squared .78 Standard error 87,127 Observations 8 What is the regression equation (total cost equation) for the above information?

Total costs = $738(Phones) + $1,473,119

The regression equation is Y = a + bX. Which of the following is true?

a represents the amount of Y when X = 0.

Automite company is an automobile replacement parts dealer in a large metropolitan community. Automite is preparing its sales forecast for the coming year. Data regarding both Automite's and industry sales of replacement parts as well as both the used and new automobile sales in the community for the last 10 years have been accumulated. If Automite wants to determine if its sales of replacement parts are patterned after the industry sales of replacement parts or to the sales of used and new automobiles, the company would employ:

correlation and regression analysis.

Regression analysis:

estimates the dependent cost variable.

A company has accumulated data for the last 24 months in order to determine if there is an independent variable that could be used to estimate shipping costs. Three possible independent variables being considered are packages shipped, miles shipped, and pounds shipped. The quantitative technique that should be used to determine whether any of these independent variables might provide a good estimate for shipping costs is:

linear regression.

For cost estimation simple regression differs from multiple regression in that simple regression uses only:

one independent variable, while multiple regression uses more than one independent variable.