Q&A Hero

Q: Below you are given a partial Excel output based on a sample of 12 observations relating the number of personal computers sold by a computer shop per month (y), unit price (x1in $1,000) and the number of advertising spots (x2) used on a local television station.CoefficientStandard ErrorIntercept17.1457.865x1-0.1043.282x21.3760.250a. Use the output shown above and write an equation that can be used to predict the monthly sales of computers.b. Interpret the coefficients of the estimated regression equation found in Part a.c. If the company charges $2,000 for each computer and uses 10 advertising spots, how many computers would you expect them to sell?d. At = 0.05, test to determine if the price is a significant variable.e. At = 0.05, test to determine if the number of advertising spots is a significant variable.

Q: The following is part of the results of a regression analysis involving sales (yin millions of dollars), advertising expenditures (x1in thousands of dollars), and number of sales people (x2) for a corporation:Source of VariationDegrees of FreedomSum of SquaresMean SquareFRegression2822.088Error7736.012a. At = 0.05 level of significance, test to determine if the model is significant. That is, determine if there exists a significant relationship between the independent variables and the dependent variable.b. Determine the multiple coefficient of determination.c. Determine the adjusted multiple coefficient of determination.d. What has been the sample size for this regression analysis?

Q: The following is part of the results of a regression analysis involving sales (yin millions of dollars), advertising expenditures (x1in thousands of dollars), and number of salespeople (x2) for a corporation. The regression was performed on a sample of 10 observations.CoefficientStandard ErrorConstant-11.34020.412x10.7980.332x20.1410.278a. Write the regression equation.b. Interpret the coefficients of the estimated regression equation found in Part (a).c. At =0.05, test for the significance of the coefficient of advertising.d. At =0.05, test for the significance of the coefficient of number of salespeople.e. If the company uses $50,000 in advertisement and has 800 salespersons, what are the expected sales? Give your answer in dollars.

Q: In order to determine whether or not the number of automobiles sold per day (y) is related to price (x1in $1,000), and the number of advertising spots (x2), data were gathered for 7 days. Part of the Excel output is shown below.ANOVAdfSSMSFRegression40.700Residual1.016CoefficientsStandard ErrorIntercept0.8051X10.49770.4617X20.47330.0387a. Determine the least squares regression function relating yto x1and x2.b. If the company charges $20,000 for each car and uses 10 advertising spots, how many cars would you expect them to sell in a day?c. At = 0.05, test to determine if the fitted equation developed in Part a represents a significant relationship between the independent variables and the dependent variable.d. At = 0.05, test to see if 1is significantly different from zero.e. Determine the multiple coefficient of determination.

Q: In order to determine whether or not the sales volume of a company (yin millions of dollars) is related to advertising expenditures (x1in millions of dollars) and the number of salespeople (x2), data were gathered for 10 years. Part of the Excel output is shown below.ANOVAdfSSMSFRegression321.11Residual63.39CoefficientsStandard ErrorIntercept7.01741.8972x18.62332.3968x20.08580.1845a. Use the above results and write the regression equation that can be used to predict sales.b. Estimate the sales volume for an advertising expenditure of 3.5 million dollars and 45 salespeople. Give your answer in dollars.c. At = 0.01, test to determine if the fitted equation developed in Part a represents a significant relationship between the independent variables and the dependent variable.d. At = 0.05, test to see if 1is significantly different from zero.e. Determine the multiple coefficient of determination.f. Compute the adjusted coefficient of determination.

Q: Shown below is a partial Excel output from a regression analysis.ANOVAdfSSMSFRegression60ResidualTotal19140CoefficientsStandard ErrorIntercept10.002.00x1-2.001.50x26.002.00x3-4.001.00a. Use the above results and write the regression equation.b. Compute the coefficient of determination and fully interpret its meaning.c. Is the regression model significant? Perform an Ftest and let = 0.05.d. At = 0.05, test to see if there is a relation between x1and y.e. At = 0.05, test to see if there is a relation between x3and y.

Q: The following results were obtained from a multiple regression analysis.Source of VariationDegrees of FreedomSum of SquaresMean SquareFRegression900Error35Total394,980a. How many independent variables were involved in this model?b. How many observations were involved?c. Determine the Fstatistic.

Q: A multiple regression analysis between yearly income (yin $1,000s), college grade point average (x1), age of the individuals (x2), and the gender of the individual (x3; zero representing female and one representing male) was performed on a sample of 10 people, and the following results were obtained using Excel.ANOVAdfSSMSFRegression360.59Residual23.91CoefficientsStandard ErrorIntercept4.09281.4400x110.02301.6512x20.10200.1225x3-4.48111.4400a. Write the regression equation for the above.b. Interpret the meaning of the coefficient of x3.c. Compute the coefficient of determination.d. Is the coefficient of x1significant? Use = 0.05.e. Is the coefficient of x2significant? Use = 0.05.f. Is the coefficient of x3significant? Use = 0.05.g. Perform an Ftest and determine whether or not the model is significant.

Q: Multiple regression analysis was used to study how an individual's income (yin thousands of dollars) is influenced by age (x1in years), level of education (x2ranging from 1 to 5), and the person's gender (x3where 0 =female and 1=male). The following is a partial result of Excel output that was used on a sample of 20 individuals.ANOVAdfSSMSFRegression84Residual112CoefficientsStandard Errorx10.62510.094x20.92100.190x3-0.5100.920a. Compute the coefficient of determination.b. Perform a t test and determine whether or not the coefficient of the variable "level of education" (i.e., x2) is significantly different from zero. Let = 0.05.c. At = 0.05, perform an Ftest and determine whether or not the regression model is significant.d. As you note the coefficient of x3is -0.510. Fully interpret the meaning of this coefficient.

Q: In order to test for the significance of a regression model involving 4 independent variables and 36 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of Farea. 4 and 36b. 3 and 35c. 4 and 31d. 4 and 32

Q: A regression analysis involved 6 independent variables and 27 observations. The critical value of t for testing the significance of each of the independent variable's coefficients will have a. 27 degrees of freedom b. 26 degrees of freedom c. 21 degrees of freedom d. 20 degrees of freedom

Q: In a multiple regression analysis involving 5 independent variables and 30 observations, SSR = 360 and SSE = 40. The coefficient of determination is a. 0.80 b. 0.90 c. 0.25 d. 0.15

Q: In order to test for the significance of a regression model involving 8 independent variables and 121 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of Fare a. 8 and 121 b. 7 and 120 c. 8 and 112 d. 7 and 112

Q: A regression model involved 18 independent variables and 200 observations. The critical value of tfor testing the significance of each of the independent variable's coefficients will have a. 18 degrees of freedom b. 200 degrees of freedom c. 199 degrees of freedom d. 181 degrees of freedom

Q: In a multiple regression analysis involving 10 independent variables and 81 observations, SST = 120 and SSE = 42. The coefficient of determination is a. 0.81 b. 0.11 c. 0.35 d. 0.65

Q: For a multiple regression model, SST = 200 and SSE = 50. The multiple coefficient of determination is a. 0.25 b. 4.00 c. 250 d. 0.75

Q: Refer to Exhibit 13-8. The estimated income of a 30-year-old male is a. $51,000 b. $5,100 c. $510 d. $51

Q: Refer to Exhibit 13-8. The model a. is significant b. is not significant c. would be significant is the sample size was larger than 30 d. None of these alternatives is correct.

Q: Refer to Exhibit 13-8. The test statistic for testing the significance of the model is a. 0.73 b. 1.47 c. 28.69 d. 5.22

Q: Refer to Exhibit 13-8. If we want to test for the significance of the model, the critical value of Fat a 5% significance level is a. 3.33 b. 3.35 c. 3.34 d. 2.96

Q: Refer to Exhibit 13-8. The multiple coefficient of determination is a. 0.32 b. 0.42 c. 0.68 d. 0.50

Q: Refer to Exhibit 13-8. The yearly income of a 24-year-old male individual is a. $13.80 b. $13,800 c. $46,800 d. $49,800

Q: Refer to Exhibit 13-8. The yearly income of a 24-year-old female individual is a. $19.80 b. $19,800 c. $49.80 d. $49,800

Q: Exhibit 13-8The following estimated regression model was developed relating yearly income (yin $1,000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female). = 30 + 0.7x1+ 3x2Also provided are SST = 1,200 and SSE = 384.Refer to Exhibit 13-8. From the above function, it can be said that the expected yearly income ofa. males is $3 more than femalesb. females is $3 more than malesc. males is $3,000 more than femalesd. females is $3,000 more than males

Q: Refer to Exhibit 13-7. The test statistic from the information provided isa. 2.110b. 3.480c. 4.710d. 6.875

Q: Refer to Exhibit 13-7. If we want to test for the significance of the model at 95% confidence, the critical Fvalue (from the table) is a. 3.06 b. 3.48 c. 3.34 d. 3.11

Q: Exhibit 13-7A regression model involving 4 independent variables and a sample of 15 periods resulted in the following sum of squares.SSR = 165SSE = 60Refer to Exhibit 13-7. The coefficient of determination isa. 0.3636b. 0.7333c. 0.275d. 0.5

Q: A multiple regression model has the form = 5 + 6x+ 7wAs x increases by 1 unit (holding wconstant), yis expected toa. increase by 11 unitsb. decrease by 11 unitsc. increase by 6 unitsd. decrease by 6 units

Q: A variable that cannot be measured in numerical terms is called a. a nonmeasurable random variable b. a constant variable c. a dependent variable d. a qualitative variable

Q: A term used to describe the case when the independent variables in a multiple regression model are correlated is a. regression b. correlation c. multicollinearity d. None of the alternative answers is correct.

Q: A regression model in which more than one independent variable is used to predict the dependent variable is called a. a simple linear regression model b. a multiple regression model c. an independent model d. None of these alternatives is correct.

Q: Refer to Exhibit 13-6. Carry out the test to determine if there is a relationship among the variables at the 5% level. The null hypothesis should a. be rejected b. not be rejected c. revised d. None of these alternatives is correct.

Q: Refer to Exhibit 13-6. The Fvalue obtained from the table used to test if there is a relationship among the variables at the 5% level equals a. 3.41 b. 3.63 c. 3.81 d. 19.41

Q: Refer to Exhibit 13-6. The test statistic used to determine if there is a relationship among the variables equals a. -1.4 b. 0.2 c. 0.77 d. 5

Q: Refer to Exhibit 13-6. The sum of squares due to error (SSE) equals a. 37.33 b. 485.3 c. 4,853 d. 6,308.9

Q: Refer to Exhibit 13-6. The degrees of freedom for the sum of squares explained by the regression (SSR) are a. 2 b. 3 c. 13 d. 15

Q: Refer to Exhibit 13-6. Carry out the test of significance for the parameter 1at the 1% level. The null hypothesis should be a. rejected b. not rejected c. revised d. None of these alternatives is correct.

Q: Refer to Exhibit 13-6. The tvalue obtained from the table which is used to test an individual parameter at the 1% level is a. 2.65 b. 2.921 c. 2.977 d. 3.012

Q: Refer to Exhibit 13-6. We want to test whether the parameter 1is significant. The test statistic equals a. -1.4 b. 1.4 c. 3.6 d. 5

Q: Refer to Exhibit 13-6. The interpretation of the coefficient of x1is that a. a one unit change in x1will lead to a 3.682 unit decrease in b. a one unit increase in x1will lead to a 3.682 unit decrease in when all other variables are held constant c. a one unit increase in x1will lead to a 3.682 unit decrease in x2when all other variables are held constant d. It is impossible to interpret the coefficient.

Q: Exhibit 13-6Below you are given a partial Excel output based on a sample of 16 observations.ANOVAdfSSMSFRegression4,8532,426.5Residual485.3CoefficientsStandard ErrorIntercept12.9244.425x1-3.6822.630x245.21612.560Refer to Exhibit 13-6. The estimated regression equation isa. y= 0+ 1x1+ 2x2+ b. E(y) = 0+ 1x1+ 2x2c. = 12.924 "‘3.682x1+ 45.216x2d. = 4.425 + 2.63x1+ 12.56x2

Q: Refer to Exhibit 13-5. Carry out the test of significance for the parameter 1at the 5% level. The null hypothesis should bea. rejectedb. not rejectedc. revisedd. None of these alternatives is correct.

Q: Refer to Exhibit 13-5. The tvalue obtained from the table to test an individual parameter at the 5% level isa. 2.06b. 2.069c. 2.074d. 2.080

Q: Refer to Exhibit 13-5. We want to test whether the parameter 1is significant. The test statistic equals a. 0.357 b. 2.8 c. 14 d. 1.96

Q: Refer to Exhibit 13-5. The interpretation of the coefficient on x1is that a. a one unit change in x1will lead to a 25.625 unit change in b. a one unit change in x1will lead to a 25.625 unit increase in when all other variables are held constant c. a one unit change in x1will lead to a 25.625 unit increase in x2when all other variables are held constant d. It is impossible to interpret the coefficient.

Q: Exhibit 13-5Below you are given a partial Excel output based on a sample of 25 observations.CoefficientsStandard ErrorIntercept145.32148.682x125.6259.150x2"‘5.7203.575x30.8230.183Refer to Exhibit 13-5. The estimated regression equation isa. y= 0+ 1x1+ 2x2+ 3x3+ b. E(y) = 0+ 1x1+ 2x2+ 3x3c. = 145.321 + 25.625x1-5.720x2+ 0.823x3d. = 48.682 + 9.15x1+ 3.575x2+ 0.183x3

Q: Refer to Exhibit 13-4. Which equation describes the multiple regression equation?abcd

Q: Refer to Exhibit 13-4. Which equation gives the estimated regression line? a b c d

Q: Exhibit 13-4a. y= 0+ 1x1+ 2x2+ b. E(y) = 0+ 1x1+ 2x2c. = bo+ b1x1+ b2x2d. E(y) = 0+ 1x1+ 2x2Refer to Exhibit 13-4. Which equation describes the multiple regression model?abcd

Q: Refer to Exhibit 13-3. The conclusion is that thea. model is not significantb. model is significantc. slope of x1is significantd. slope of x2is significant

Q: Refer to Exhibit 13-3. The critical Fvalue at 95% confidence is a. 2.53 b. 2.69 c. 2.76 d. 2.99

Q: Refer to Exhibit 13-3. The computed Fstatistic for testing the significance of the above model is a. 43.75 b. 0.875 c. 50.19 d. 7.00

Q: Exhibit 13-3In a regression model involving 30 observations, the following estimated regression equation was obtained: = 17 + 4x1" 3x2+ 8x3+ 8x4For this model SSR = 700 and SSE = 100.Refer to Exhibit 13-3. The coefficient of determination for the above model is approximatelya. -0.875b. 0.875c. 0.125d. 0.144

Q: Refer to Exhibit 13-2. The multiple coefficient of determination for this problem isa. 0.4368b. 0.6960c. 0.3040d. 0.2289

Q: Refer to Exhibit 13-2. If SSR = 600 and SSE = 300, the test statistic Fis a. 2.33 b. 0.70 c. 17.5 d. 1.75

Q: Refer to Exhibit 13-2. If we want to test for the significance of the regression model, the critical value of Fat 95% confidence is a. 3.68 b. 3.29 c. 3.24 d. 4.54

Q: Refer to Exhibit 13-2. The coefficient of x2indicates that if television advertising is increased by $1 (holding the unit price constant), sales are expected to a. increase by $5 b. increase by $12,000 c. increase by $5,000 d. decrease by $2,000

Q: Exhibit 13-2A regression model between sales (y in $1,000), unit price (x1in dollars) and television advertisement (x2in dollars) resulted in the following function: = 7 " 3x1+ 5x2For this model SSR = 3500, SSE = 1500, and the sample size is 18.Refer to Exhibit 13-2. The coefficient of the unit price indicates that if the unit price isa. increased by $1 (holding advertising constant), sales are expected to increase by $3b. decreased by $1 (holding advertising constant), sales are expected to decrease by $3c. increased by $1 (holding advertising constant), sales are expected to increase by $4,000d. increased by $1 (holding advertising constant), sales are expected to decrease by $3,000

Q: In order to test for the significance of a regression model involving 14 independent variables and 255 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of Farea. 14 and 255b. 255 and 14c. 13 and 240d. 14 and 240

Q: A regression analysis involved 17 independent variables and 697 observations. The critical value of tfor testing the significance of each of the independent variable's coefficients will have a. 696 degrees of freedom b. 16 degrees of freedom c. 713 degrees of freedom d. 714 degrees of freedom

Q: In a multiple regression analysis involving 12 independent variables and 166 observations, SSR = 878 and SSE = 122. The coefficient of determination is a. 0.1389 b. 0.1220 c. 0.878 d. 0.7317

Q: In a multiple regression model, the error term  is assumed to a. have a mean of 1 b. have a variance of zero c. have a standard deviation of 1 d. be normally distributed

Q: In multiple regression analysis, a. there can be any number of dependent variables but only one independent variable b. there must be only one independent variable c. the coefficient of determination must be larger than 1 d. there can be several independent variables, but only one dependent variable

Q: In a multiple regression model, the values of the error term ,, are assumed to be a. zero b. dependent on each other c. independent of each other d. always negative

Q: In multiple regression analysis, the correlation among the independent variables is termed a. homoscedasticity b. linearity c. multicollinearity d. adjusted coefficient of determination

Q: The adjusted multiple coefficient of determination is adjusted for a. the number of dependent variables b. the number of independent variables c. the number of equations d. detrimental situations

Q: In a multiple regression model, the variance of the error term  is assumed to be a. the same for all values of the dependent variable b. zero c. the same for all values of the independent variable d. -1

Q: The ratio of MSE/MSR yields a. SST b. the Fstatistic c. SSR d. None of these alternatives is correct.

Q: In a multiple regression analysis SSR = 1,000 and SSE = 200. The Fstatistic for this model is a. 5.0 b. 1,200 c. 800 d. Not enough information is provided to answer this question.

Q: Refer to Exhibit 13-1. The computed Fstatistics for testing the significance of the above model is a. 1.500 b. 20.00 c. 0.600 d. 0.6667

Q: Refer to Exhibit 13-1. MSR for this model is a. 200 b. 10 c. 1,000 d. 43

Q: Exhibit 13-1In a regression model involving 44 observations, the following estimated regression equation was obtained. = 29 + 18x1+43x2+ 87x3For this model SSR = 600 and SSE = 400.Refer to Exhibit 13-1. The coefficient of determination for the above model isa. 0.667b. 0.600c. 0.336d. 0.400

Q: The correct relationship between SST, SSR, and SSE is given bya. SSR = SST + SSEb. SSR = SST - SSEc. SSE = SSR - SSTd. None of these alternatives is correct.

Q: A measure of goodness of fit for the estimated regression equation is the a. multiple coefficient of determination b. mean square due to error c. mean square due to regression d. sample size

Q: A multiple regression model has a. only one independent variable b. more than one dependent variable c. more than one independent variable d. at least 2 dependent variables

Q: A multiple regression model has the form = 7 + 2x1+ 9x2 As x1increases by 1 unit (holding x2constant), yis expected to a. increase by 9 units b. decrease by 9 units c. increase by 2 units d. decrease by 2 units

Q: The multiple coefficient of determination is a. MSR/MST b. MSR/MSE c. SSR/SST d. SSE/SSR

Q: In regression analysis, the response variable is the a. independent variable b. dependent variable c. slope of the regression function d. intercept

Q: In a multiple regression model, the error term  is assumed to be a random variable with a mean of a. zero b. -1 c. 1 d. any value

Q: A variable that takes on the values of 0 or 1 and is used to incorporate the effect of qualitative variables in a regression model is called a. an interaction b. a constant variable c. a dummy variable d. None of these alternatives is correct.