# A researcher is trying to understand the relationship between employees’ salary and other relevant factors.

A researcher is trying to understand the relationship between employees’ salary and other relevant factors. A sample of 80 employees contains their current annual salary (in dollars), their years of experience in the industry (YrsExp), their years of experience with this company (YrsHere) and current level in the company (Level), coded 1 to 4, where 1 indicates the lowest level and 4 the highest. The estimated regression model for salary is given below.

Regression results for Salary

Summary measures

R-Square

0.91

0.90

Regression coefficients

Coefficient

Std Err

t-value

p-value

Constant

29583.42

1485.26

19.92

0.00

YrsExper

961.79

406.10

1.80

0.07

YrsHere

80.51

432.34

0.19

0.85

Level_2

13589.96

1531.47

8.87

0.00

Level_3

26710.24

2133.65

12.52

0.00

Level_4

50653.38

2264.73

22.37

0.00

Flag this QuestionQuestion 11pts

This question references Scenario 1.

Based on the estimated regression model, what proportion of variation in salary is explained by the model?

95%91%90%5%74%

Flag this QuestionQuestion 21pts

This question references Scenario 1.

Consider the variable years of industry experience (YrsExper). An appropriate economic interpretation of the associated coefficient 961.79 is

For each additional year of industry experience, an employee’s salary decreases by \$961.79.For each additional year of industry experience, an employee’s salary increases by \$961.79.For each additional year of industry experience, salary increases by \$961.79 for employees at level 1.For each additional year of industry experience, salary increases by \$961.79 for level-1 employees with at least 10 years of experience with the company.For two employees with the same years of experience with the company and same level in the company, the second employee’s salary will be higher by \$961.79 if he has an additional year of industry experience.

Flag this QuestionQuestion 31pts

This question references Scenario 1.

Consider again the variable years of industry experience (YrsExper). With 95% confidence, what is the least amount of salary-increase that an employee can expect for an additional year of industry experience (after controlling for all other factors)?

\$1773.98\$961.79\$812.19\$149.60None of the above.

Flag this QuestionQuestion 41pts

This question references Scenario 1.

Based on the regression model above, is years of industry experience (YrsExper) useful for explaining a manager’s salary? (Use 5% significance level)

YesNoCan’t say.

Flag this QuestionQuestion 51pts

This question references Scenario 1.

What is the estimated salary for a level 1 employee with 10 years of industry experience and 8 years of experience with this company? (Pick the closest number)

Approximately \$10,000Approximately \$30,000Approximately \$40,000Approximately \$90,000Approximately \$100,000

Flag this QuestionQuestion 61pts

This question references Scenario 1.

What is the difference in average salary between a level 1 employee and a level 3 employee? (Round to the nearest \$1,000)

\$51,000\$30,000\$27,000\$14,000\$1,000

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Scenario 2

A manager is trying to understand the relationship between the amount of money spent advertising a product (in thousands of dollars) and sales (in millions of dollars) using data for 8 months. The manager runs a regression model and obtains the following output. Notice that both sales and advertising are log-transformed.

Regression results for Log(Sales)

Summary measures

R-Square

0.9984

0.9981

Regression coefficients

Coefficient

Std Err

t-value

p-value

Constant

1.4009

0.0103

135.8713

0.0000

0.2022

0.0033

61.2021

0.0000

Flag this QuestionQuestion 71pts

This question references Scenario 2.

At the 5% level of significance, is (log-) advertising useful for explaining sales?

YesNoCan’t say.

Flag this QuestionQuestion 81pts

This question references Scenario 2.

Would your answer in the previous question change if you conducted the test at the 1% level of significance?

YesNoCan’t say.

Flag this QuestionQuestion 91pts

This question references Scenario 2.

Consider the number 0.2022 in the column titled “Coefficient”. Provide a precise economic interpretation for this number.

As advertising expenditures increase by \$1, sales increase by \$0.2022.As advertising expenditures increase by 1%, sales increase by 0.2022%.As advertising expenditures increase by 1%, sales increase by 0.002022%.As advertising expenditures increase by 1%, sales increase by \$0.2022.None of he above.

Flag this QuestionQuestion 101pts

This question references Scenario 2.

Construct a 95% confidence interval for the coefficient of Log(Advertising). The confidence interval equals…

(0.202; 1.401)(0.171; 0.233)(0.196; 0.209)(0.192; 0.212)None of the above.

Flag this QuestionQuestion 111pts

This question references Scenario 2.

If advertising expenditures are set at 20 thousand dollars, then estimated sales are (pick the closest number!)

Approximately \$231 millionApproximately 150 millionApproximately \$7 millionApproximately \$5 millionApproximately \$4 million

Flag this QuestionQuestion 121pts

This question references Scenario 2.

What percentage of the total variation in sales is not explained by advertising?

More than 99%50%6%2%Less than 1%

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Scenario 3

A manager for a large software company wants to study the factors that affect her company’s sales across different regions of the US. A recently collected database contains a random sample of 135 sales regions. For each of these regions, data is available on the region’s sales (Y, in dollars), the average price in that region (X1, in dollars), average marketing expenditures in that region (X2, in dollars), and the median household income level for the region (X3). Median household income level is coded as X3=0 if income level is low, and X3=1 if it is high.

The manager has several conjectures about the company’s sales. Using the variable notations Y, X1, X2 and X3, you are asked to construct and interpret a regression model that enables the testing of the manager’s conjectures.

Flag this QuestionQuestion 131pts

This question references Scenario 3.

She conjectures that for each increase in price by 1%, sales decrease by at least \$15,000. In order to enable the testing of her conjecture, the regression model has to include the following variables

Log(Y) and Log(X1)Log(Y) and X1Y and Log(X1)Y and X1None of the above

Flag this QuestionQuestion 141pts

This question references Scenario 3.

She also conjectures that for every additional dollar spent on marketing, the rate of sales increase is higher in regions with higher median household income levels. In order to enable the testing of her conjecture, the regression model has to include the following variables

X2 and X3X2, X3 and X2*YX2, X3 and X3*log(Y)X2, X3 and X2*X3X2,X3 and log(X1)*X2

Flag this QuestionQuestion 151pts

This question references Scenario 3.

Consider the regression model Y=a+b2X2+b3X3. Based on that model, provide a precise economic interpretation for the coefficient b2.

For every increase in marketing expenditures by \$1, sales increase/decrease by \$.For every increase in marketing expenditures by \$1, sales increase/decrease by (100)( )%For every increase in marketing expenditures by \$1, sales in low median household income regions increase/decrease by (100)()%For every increase in marketing expenditures by 1%, sales in low median household income regions increase/decrease by \$.None of the above.

Flag this QuestionQuestion 161pts

This question references Scenario 3.

Consider the regression model Y=a+b2X2+b3X3. The manager conjectures that sales are higher in high median household income regions. Based on this conjecture, which of the following is true:

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Scenario 4

Quarterly sales (in millions of dollars) are available for a large soft-drink company between Q1-94 and Q4-03. That is, starting at Q1-94 (t=1) the data contains sales for 40 consecutive quarters, ending with the most recent quarter Q4-03 (t=40). You are asked to use the data to develop a forecasting model for Q1-04. You define a dummy variable for the first quarter: Q-type1=1 if the quarter number is 1; Q-type1=0 otherwise. Similarly you define dummy variables for the other three quarters. The regression printout below summarizes your model.

Regression results for Sales

Summary measures

R-Square

0.91

0.90

Regression coefficients

Coefficient

Std Err

t-value

p-value

Constant

1320.55

128.37

10.29

0.00

T

70.65

4.04

17.51

0.00

Q-type_1

-190.42

131.69

-1.45

0.16

Q-type_2

416.37

131.38

3.17

0.00

Q-type_3

329.81

131.19

2.51

0.02

Flag this QuestionQuestion 171pts

This question references Scenario 4.

Consider the number 70.65 in the column “Coefficient”. Provide an economic interpretation for this number.

Sales increase by \$70.65 million in each quarter.Detrended sales increase by \$70.65 million in each quarter.Seasonally adjusted sales increase by \$70.65 million in every year.Sales increase by \$70.65 million in the fourth quarter of every year.None of the above.

Flag this QuestionQuestion 181pts

This question references Scenario 4.

Consider the number 416.37 in the column “Coefficient”. Provide an economic interpretation for this number.

Seasonally adjusted sales increase by \$416.37 million between Q2 and Q4.Detrended sales increase by \$416.37 million between Q2 and Q3.Sales increase by \$416.37 million between Q2 and Q4.Sales increase by \$416.37 million in Q2.None of the above.

Flag this QuestionQuestion 191pts

This question references Scenario 4.

Using the above regression model, predict sales in Q1-04. (Round to the nearest \$1Million).

\$1201 million\$3956 million\$4027 million\$4217 millionNone of the above.

Flag this QuestionQuestion 201pts

This question references Scenario 4.

Using the above regression model, predict sales in Q4-04. (Round to the nearest \$1Million).

\$3498 million\$4428 million\$4238 million\$4146.millionNone of the above.

Flag this QuestionQuestion 211pts

This question references Scenario 4.

Comparing predictions for the 5 quarters Q1-06, Q2-06, Q3-06, Q4-06 and Q1-07, which quarter would have the highest predicted sales?

Q1-06Q2-06Q3-06Q4-06Q1-07

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Scenario 5

A company designs a new laptop computer and wants to investigate customers’ preferences with respect to three select laptop features. The features are

• Price (High vs. low)
• Processor Speed (Low vs. medium vs. high)
• Weight (Low vs. high)

The company asks customers to rank products with different feature-combinations and record a preference rating. The following regression model (table below) relates ratings with features. Notice that features are entered into the regression model as dummy variables. Specifically, the dummies are coded as

• Price_High = 1 if price is high and =0 otherwise
• Speed_High = 1 if speed is high and =0 otherwise
• Speed_Medium = 1 if speed is medium and =0 otherwise
• Weight_Low = 1 if weight is low and =0 otherwise

Regression results for customers’ preference ratings are given below. Notice that the results only show the a partial regression table (i.e. there are no standard errors or p-values).

Partial Regression Results

Summary Measures

R-squared

0.70

0.64

Regression Coefficients

(Intercept)

16.10

Price_High

-4.60

Speed_High

3.70

Speed_Medium

1.30

Weight_Low

5.20

Flag this QuestionQuestion 221pts

This question references Scenario 5.

Based on the above table, what is the average rating for a laptop computer with high price, low processor speed and high weight?

16.1011.5018.0020.4025.00

Flag this QuestionQuestion 231pts

This question references Scenario 5.

Based on the above table, comparing two laptops, the first one with low weight, low processor speed and low price, and the second one with high weight, low processor speed and low price, by how much is the average rating of the second laptop different? (I.e. report the absolute value of the difference)

By 16.10By 4.60By 5.20By 3.70None of the above

Flag this QuestionQuestion 241pts

This question references Scenario 5.

Which combination of features gives the highest customer rating?

Low price, medium processor speed, low weightLow price, high processor speed, high weightLow price, low processor speed, low weightHigh price, high processor speed, low weightLow price, high processor speed, low weight

Flag this QuestionQuestion 251pts

This question references Scenario 5.

Provide an economic interpretation of the coefficient of “Speed_High”.

The rating of a laptop with high processor speed is on average 3.70 points higher compared to a laptop with medium processor speed, all else equal.The rating of a laptop with high processor speed is on average 3.70 points higher compared to a laptop with low processor speed, all else equal.The rating of a laptop with high processor speed is on average 3.70 points higher compared to a laptop with high price, all else equal.The rating of a laptop with high processor speed is on average 3.70 points higher compared to a laptop with low weight, all else equal.None of the above.

Flag this QuestionQuestion 261pts

This question references Scenario 5.

Based on economic considerations, the company cannot offer the low price in combination with the high processor speed. Within these constraints, which combination of features now gives the highest customer rating?

Low price, medium processor speed, low weight.Low price, high processor speed, high weight.Low price, low processor speed, low weight.High price, high processor speed, low weightLow price, low processor speed, high weight

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Scenario 6

East Meadow is a suburban New York community. A real-estate company gathers data on appraised values of single-family houses (recorded in thousands of dollars) based on the age of the house, whether or not it has a fireplace, and whether or not it has a finished basement. The table below shows a regression model relating a house’s value to the predictor variables

• Bed (=number of bedrooms),
• Bath (=number of bathrooms),
• Age (=age of the house, in years),
• Basement (=1 if basement is finished and =0 otherwise)

Regression results for customers’ house values are given below. Notice that the results only show the a partial regression table (i.e. there are no standard errors or p-values).

Summary Measures

R-squared

0.53

0.49

Regression Coefficients

(Intercept)

-18.20

Bed

6.60

Bath

36.40

Age

-3.50

Basement

17.40

Age*Basement

1.50

Flag this QuestionQuestion 271pts

This question references Scenario 6.

Based on the regression table, what is the estimated value of a house with 2 bedrooms, 2 bathrooms, 10 years old and unfinished basement?

\$86 thousand\$51 thousand\$47.8 thousand\$32.8 thousandNone of the above

Flag this QuestionQuestion 281pts

This question references Scenario 6.

Based on the regression table, provide an economic interpretation for the coefficient for “Bed”.

For every additional bedroom, a house’s value increases by \$6.60 thousand, if all other variables remain constant.For every additional bedroom, a house’s value increases by \$6.60/18.2 thousand = \$0.36 thousand, if all other variables remain constant.For every additional bedroom, a house’s value increases by \$(6.60 + 36.4*number of bathrooms) thousand, if all other variables remain constant.For every additional bedroom, a house’s value decreases by \$18.20 thousand, if all other variables remain constant.Adding two additional bedrooms, a house’s value increases by \$6.60 thousand, if all other variables remain constant.

Flag this QuestionQuestion 291pts

This question references Scenario 6.

Provide an economic interpretation for the coefficient for “Age”

All else equal, houses depreciate (=decrease in value), on average, at a rate of \$3.5 thousand for each additional year of age.All else equal, houses depreciate (=decrease in value), on average, at a rate of \$2 thousand for each additional year of age.All else equal, houses with an unfinished basement depreciate (=decrease in value), on average, at a rate of \$3.5 thousand for each additional year of age.All else equal, houses with a finished basement depreciate (=decrease in value), on average, at a rate of \$3.5 thousand for each additional year of age.All else equal, houses with a finished basement, 2 bedrooms and 2 bathrooms depreciate (=decrease in value), on average, at a rate of \$3.5 thousand for each additional year of age.

Flag this QuestionQuestion 301pts

This question references Scenario 6.

Provide an economic interpretation for the coefficient of “Age*Basement.

All else equal, houses with an unfinished basement depreciate (=decrease in value), on average, at a rate of \$1.5 thousand per year slower than houses with finished basement.All else equal, houses with a finished basement depreciate (=decrease in value), on average, at a rate of \$1.5 thousand per year slower than houses with unfinished basement.All else equal, houses with a finished basement depreciate (=decrease in value), on average, at a rate of \$1.5 thousand for each additional year of age.All else equal, houses with an unfinished basement depreciate (=decrease in value), on average, at a rate of \$1.5 thousand for each additional year of age.The coefficient has no economic meaningful interpretation!

Flag this QuestionQuestion 311pts

This question references Scenario 6.

The analyst has additional information available on whether or not the house has a swimming pool (denoted by the variable “Pool” which equals 1 if the house has a pool and equals 0 otherwise). The analyst conjectures that the rate of depreciation for each additional year of age is faster for houses without a pool. In order to investigate that specific conjecture, the analyst has to…

a…. include the variable “Pool” into the above regression model.b…. include the variable “Basement*Pool” into the above regression model.c…. include the variable “Age*Pool” into the above regression model.d…. include the variable “Exp(Pool)” into the above regression model.e…. include the variable “Log(Pool)” into the above regression model.

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Scenario 7

Officials in a small town are preparing the annual budget for their community. As one component of this preparation, they want to estimate the proportion of their constituents that file fraudulent tax returns. Due to cost and time constraints they decide to only sample a representative subset of taxpayers and scrutinize their tax returns.

Flag this QuestionQuestion 321pts

This question references Scenario 7.

The town officials believe that if the proportion of fraudulent tax returns is higher than 5%, then increased administrative action against fraudulent tax filing is necessary. A 95% confidence interval for the proportion of fraudulent tax returns yields (2.75%; 6.12%). Based on this interval, what is the town officials’ decision regarding administrative action against fraudulent tax filing?

Increase administrative action against fraudulent tax filing.Leave administrative action against fraudulent tax filing as is.Reduce administrative action against fraudulent tax filing.Inconclusive. Need more information to make a decision.

Flag this QuestionQuestion 331pts

This question references Scenario 7.

How would the answer from the previous question change if the 95% confidence interval was (5.50%; 7.34%)?

We would now decide to increase administrative action against fraudulent tax filing.We would now decide to leave administrative action against fraudulent tax filing as is.We would now decide to reduce administrative action against fraudulent tax filing.Still inconclusive. Still need more information to make a decision.

Flag this QuestionQuestion 341pts

This question references Scenario 7.

The town officials are not satisfied with the accuracy of the confidence interval (2.75%; 6.12%) obtained in question 32. What are the options to increase the interval’s accuracy (at the same confidence level)?

To increase the sample size.To reduce the sample size.To use a smaller multiple.To use a larger multiple.There are no options to increase the accuracy

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A researcher is trying to understand the relationship between employees’ salary and other relevant factors. was first posted on September 14, 2020 at 9:48 pm.