EBK BUSINESS STATISTICS
8th Edition
ISBN: 9780135179833
Author: STEPHAN
Publisher: VST
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A manager at a local bank analyzed the relationship between monthly salary and three independent variables: Length of service
(measured in months), Gender (0 = female, 1 = male), and Job type (0 = clerical, 1 = technical). The following ANOVA summarizes the
%D
regression results.
ANOVA
Source of Variation
df
Sum of Squares
Mean Square
F
Regression
3
1,004,346.771
334,782.257
5.96
Residual
26
1,461,134.596
56,197.48445
Total
29
2,465,481.367
Coefficients
Standard Error
t-Stat
p-value
Intercept
784.92
322.25
2.44
0.02
Service
9.19
3.20
2.87
0.01
Gender
222.78
89.00
2.50
0.02
Job
-28.21
89.61
-0.31
0.76
Based on the ANOVA and a O.05 significance level, the global null hypothesis test of the multiple regression model
A manager at a local bank analyzed the relationship between monthly salary and three independent variables: Length of service
(measured in months), Gender (0 = female, 1= male), and Job type (0 = clerical, 1 = technical). The following ANOVA summarizes the
%3D
regression results.
ANOVA
Source of Variation
df
Sum of Squares
Mean Square
F
Regression
3
1,004,346.771
334,782.257
5.96
Residual
26
1,461,134.596
56,197.48445
Total
29
2,465,481.367
Coefficients
Standard Error
t-Stat
p-value
Intercept
784.92
322.25
2.44
0.02
Service
9.19
3.20
2.87
0.01
Gender
222.78
89.00
2.50
0.02
Job
-28.21
89.61
-0.31
0.76
The level of significance is 0.05. In the regression model, which of the following are dummy variables?
As a marketing manager for TriFood, you want to determine whether store Sales (# sold in one month) of TriPower bars are related to price (in cents) of TriPower bars and in-store promotional expenditures (in dollars) for TriPower bars. You conduct a multiple regression analysis with store Sales (Y) as the response variable, and Price (X1) and Promotion (X2) as explanatory variables. Use the pictured Excel regression output below to answer the questions.
a) Interpret the value for R square. Interpret the estimated coefficient for price.
b) State the hypotheses for assessing the statistical significance of the overall regression equation. Does the model overall fit the data (yes or no?)
f) An external consultant to TriFoods believes that for every $1 increase in promotional expenditures, sales will increase by 4.7 units. Test the consultant's hypothesis at a 5% significance level using both approaches (tcalc vs tcrit and p-value vs a).
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- As a marketing manager for TriFood, you want to determine whether store Sales (# sold in one month) of TriPower bars are related to price (in cents) of TriPower bars and in-store promotional expenditures (in dollars) for TriPower bars. You conduct a multiple regression analysis with store Sales (Y) as the response variable, and Price (X1) and Promotion (X2) as explanatory variables. Use the pictured Excel regression output below to answer the questions. a) Write the estimated multiple regression equation. b) Should one interpret the estimated value for the intercept (yes or no)? c) Interpret the value for Standard Error under Regression Statistics. d) Interpret the value for R square. e) State the hypotheses for assessing the statistical significance of the overall regression equation. f) Interpret the estimated coefficient for price. g) An external consultant to TriFoods believes that for every $1 increase in promotional expenditures, sales will increase by 4.7 units. Test the…arrow_forwardA manager at a local bank analyzed the relationship between monthly salary and three independent variables: Length of service (measured in months), Gender (0 = female, 1 = male), and Job type (0 = clerical, 1 = technical). The following ANOVA summarizes the regression results.ANOVA Source of Variation df Sum of Squares Mean Square F Regression 3 1,004,346.771 334,782.257 5.96 Residual 26 1,461,134.596 56,197.48445 Total 29 2,465,481.367 Coefficients Standard Error t-Stat p-value Intercept 784.92 322.25 2.44 0.02 Service 9.19 3.20 2.87 0.01 Gender 222.78 89.00 2.50 0.02 Job −28.21 89.61 −0.31 0.76 The level of significance is 0.05. Based on the hypothesis tests for the individual regression coefficients, ________. Multiple Choice all the regression coefficients are not equal to zero "Job" is the only significant variable in the model only months of service and gender are significantly related to monthly salary "Service"…arrow_forwardThe chairman of the marketing department at a university undertakes a study to relate starting salary (dependent variable) measured in thousands of dollars to grade point average (GPA) which is the independent variable. He receives the following result: GPA Starting salary 3.26 33.8 2.60 23.8 3.35 33.5 2.86 30.4 3.82 39.4 Calculate the regression line. Test if the independent variable has a significant effect on the dependent variable at u=o.l. Calculate the multiple coefficient of determination and interpret it in words.arrow_forward
- The accompanying data represent the number of days absent, x, and the final exam score, y, for a sample of college students in a general education course at a large state university. Complete parts (a) through (e) below. Click the icon to view the absence count and final exam score data. Click the icon to view a table of critical values for the correlation coefficient. ..... (a) Find the least-squares regression line treating number of absences as the explanatory variable and the final exam score as the response variable. %3D + (Round to three decimal places as needed.) (b) Interpret the slope and the y-intercept, if appropriate. Choose the correct answer below and fill in any answer boxes in your choice. (Round to three decimal places as needed.) Question Viewer O A. For every additional absence, a student's final exam score drops points, on average. It is not appropriate to interpret the y-intercept. B. For every additional absence, a student's final exam score drops points, on…arrow_forwardThe local utility company surveys 12 randomly selected customers. For each survey participant, the company collects the following: annual electric bill (in dollars) and home size (in square feet). Output from a regression analysis appears below: Bill = 15.9 + 4.45*Size Coefficients Estimate Std. Error (Intercept) 15.9 0.3 Size 4.45 0.57 We are 98% confident that the mean annual electric bill increases by between dollars and dollars for every additional square foot in home size.arrow_forwardThe following table shows the starting salary and profile of a sample of 10 employees in a certain call center agency. Run a multiple regression analysis with starting salary as the dependent variable (pesos) and GPA, years of experience and civil service ratings as the independent variables. Use .05 level of significance.Which of the given independent variables is/are significant? * avil Years of Starting salary GPA service experience ratings 79.5 15000 80.1 15000 81.2 1 1 78.0 15500 81.3 16000 82.4 2 3 79.0 80.0 85.0 16200 83.4 3 17500 87.9 89.9 89.1 84.1 89.0 89.2 4 18000 90.3 5 16,300 84.2 3 17000 87.0 4 17900 88.1 GPA and years of experience GPA, years of experience and civil service ratings intercept, GPA, years of experience and civil service ratings O years of experience and civil service ratingsarrow_forward
- The local utility company surveys 11 randomly selected customers. For each survey participant, the company collects the following: annual electric bill (in dollars) and home size (in square feet). Output from a regression analysis appears below: Bill = 12.4 +4.54*Size Coefficients Estimate Std. Error (Intercept) 12.4 Size 4.54 0.6 0.85 dollars and We are 80% confident that the mean annual electric bill increases by between dollars for every additional square foot in home size. Round your answers to three decimal places and enter in increasing order.arrow_forwarddo fastarrow_forwardZagat’s publishes restaurant ratings for various locations in the United States. The following table contains the Zagat rating for food, décor, service, and the cost per person for a sample of 100 restaurants located in New York City and in a suburb of New York City. Develop a regression model to predict the cost per person, based on a variable that represents the sum of the ratings for food, décor, and service. Predict the mean cost per person for a restaurant with a sum-mated rating of 50. What should you tell the owner of a group of restaurants in this geographical area about the relationship between the summated rating and the cost of a meal? Location Food Décor Service Summated Rating Coded Location Cost Bins Midpoints City 22 14 19 55 0 33 19.99 25 City 20 15 20 55 0 26 29.99 35 City 23 19 21 63 0 43 39.99 45 City 19 18 18 55 0 32 49.99 55 City 24 16 18 58 0 44 59.99 65 City 22 22 21 65 0 44 69.99 75 City 22 20 20 62 0 50 79.99 85 City 20 19…arrow_forward
- We are interested in the relationship between mid-term exam scores and final exam scores. The Final Exam score is the dependent variable and Midterm score is the independent variable. Use the simple regression output on below to answer the question below. Use a significance level of 0.05 for all hypothesis tests and intervals. What proportion of the variation in the Final Exam scores is not "explained" by the simple linear relationship with Midterm score? Analysis of Variance Sum of Source DF Squares Mean Square F Ratio Model 1 2632.8012 2632.80 23.2115 Error 54 6125.0381 113.43 Prob > F C. Total 55 8757.8393 It| Lower 95% Upper 95% Intercept 31.738559 10.26099 Midterm 3.09 0.0031* 11.166522 52.310596 0.61916 0.128514 4.82 <.0001* 0.3615044 0.8768157arrow_forwardThe regional transit authority for a major metropolitan area wants to determine whetherthere is a relationship between the age of a bus and the annual maintenance cost. A sampleof ten buses resulted in the following data: a. Develop a scatter chart for these data. What does the scatter chart indicate about therelationship between age of a bus and the annual maintenance cost?b. Use the data to develop an estimated regression equation that could be used to predictthe annual maintenance cost given the age of the bus. What is the estimated regressionmodel?c. Test whether each of the regression parameters b0 and b1 is equal to zero at a 0.05level of significance. What are the correct interpretations of the estimated regressionparameters? Are these interpretations reasonable?d. How much of the variation in the sample values of annual maintenance cost does themodel you estimated in part b explain?e. What do you predict the annual maintenance cost to be for a 3.5-year-old bus?arrow_forwardDo movies of different types have different rates of return on their budgets? Here's a regression of USGross (SM) on Budget for comedies and action movies with an indicator variable. Complete parts (a) through (d). Dependent variable is: USGross ($M) Coefficient SE(Coeff) - 6.78278 16.95 1.00523 Variable Constant Budget ($M) Comedy 24.0373 0.1613 11.73 t-ratio P-value -0.400 0.6907 6.23 <0.0001 2.05 0.0451 a) Write out the regression model. USGross = + ( Budget + (Comedy R-squared = 32.8% R-squared (adjusted) = 31.0% s = 47.51 55 degrees of freedomarrow_forward
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