A multiple regression model has the form
y-estimeted =11+6X+12W
As X increases by 1 unit (holding W constant), Y is expected to
Question 1 options:
| increase by 11 units | |
| decrease by 11 units | |
| decrease by 6 units | |
| increase by 6 units |
If the coefficient of determination is a positive value, then the coefficient of correlation
Question 2 options:
| must be zero | |
| can be either negative or positive | |
| must be larger than 1 | |
| must also be positive |
In a multiple regression analysis involving 15 independent variables and 200 observations, SST = 800 and
SSE = 240. The coefficient of determination isQuestion 3 options:
| 0.300 | |
| 0.192 | |
| c.0.500 | |
| 0.700 |
In regression analysis, the variable that is being predicted is the
Question 4 options:
| dependent variable | |
| independent variable | |
| is usually x | |
| intervening variable |
A measure of goodness of fit for the estimated regression equation is theQuestion 5 options:
| sample size | |
| mean square due to regression | |
| mean square due to error | |
| multiple coefficient of determination |
In a regression model involving more than one independent variable, which of the following tests must be used in order to determine if the relationship between the dependent variable and the set of independent variables is significant?Question 6 options:
| t test | |
| Either a t test or a chi-square test can be used | |
| F test | |
| chi-square test |
In order to test for the significance of a regression model involving 5 independent variables and 47 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F areQuestion 7 options:
| 47 and 3 | |
| 5 and 41 | |
| 3 and 47 | |
| 2 and 43 |
Correlation analysis is used to determineQuestion 8 options:
| a multiple regression model | |
| a specific value of the dependent variable for a given value of the independent variable | |
| the equation of the regression line | |
| the strength of the relationship between the dependent and the independent variables |
The interval estimate of the mean value of y for a given value of x isQuestion 9 options:
| confidence interval estimate | |
| prediction interval estimate | |
| average regression | |
| x versus y correlation interval |
In a regression analysis, the coefficient of determination is 0.4225. The coefficient of correlation in this situation isQuestion 10 options:
| 0.1785 | |
| 0.65 | |
| any positive value | |
| 0.125 |
Case 1
A study intends to measure the effect of home size and neighborhood rating on sales price. The data are presented below:
| Sales Price | Home Size | Rating |
| 180.0 | 23 | 5 |
| 98.1 | 11 | 2 |
| 173.1 | 20 | 9 |
| 136.5 | 17 | 3 |
| 141.0 | 15 | 8 |
| 165.9 | 21 | 4 |
| 193.5 | 24 | 7 |
| 127.8 | 13 | 6 |
| 163.5 | 19 | 7 |
| 172.5 | 25 | 2 |
| Sample correlation (Home Size, Rating) | 0.043254 |
| Sample correlation (Home Size, Sales Price) | 0.937858 |
| Sample correlation (Rating, Sales Price) | 0.372738 |
Based on the Excel Regression Analyses output (you have to make it in Excel) answer the following questions. Use α = .05.
ANOVA: select the correct statement (use α=.05):Question 11 options:
| Since the significance of the model is 9.57E-08, we reject Ho, and conclude that at least one independent variable is related to Sales Price at alpha is 0.05. | |
| Since the significance of the model is 9.57E-08, we do not reject Ho, and conclude that at least one independent variable is related to Sales Price. | |
| Since the significance of the model is 9.57E-08, we reject Ho, and conclude that the two independent variables are related to Sales Price. | |
| Since the significance of the model is 9.57E-08, we do not reject Ho, and conclude that the independent variables are not related to Sales Price. |
Case 1 (continued)
t test. Select the correct conclusion for individual significance testing.Question 12 options:
| Since the p-value (4.73E-08) is less than α (.05), we do not reject Ho, and conclude that Home Size is not related to Sales Price | |
| Since the p-value (4.73E-08) is less than α (.05), we reject Ho, and conclude that Home Size is related to Sales Price at 95% confidence | |
| Since the p-value (4.73E-08) is less than α (.05), we do not reject Ho, and conclude that Home Size is related to Sales Price | |
| Since the p-value (4.73E-08) is less than α (.05), we reject Ho, and conclude that Home Size is not related to Sales Price |
Case 1 (continued)
Coefficients: select the correct statement:Question 13 options:
| Sales Price increases in one dollar when rating increases in 3.83 points. | |
| Sales Price increases in 3.83 dollars when rating increases in 1 point. | |
| Sales Price decreases in one dollar when rating increases in 3.83 points. | |
| Sales Price decreases in 3.83 dollars when rating increases in 1 point. |
Case 1
Multicollinearity: select the correct statement:Question 14 options:
| Since the absolute value of correlation (Home Size, Sales Price) is greater than .7, there is a problem of multicollinearity. | |
| Since the absolute value of correlation (Home Size, Rating) is less than .7, there is a problem of multicollinearity. | |
| Since the absolute value of correlation (Home Size, Sales Price) is greater than .7, there is not a problem of multicollinearity. | |
| Since the absolute value of correlation (Home Size, Rating) is less than .7, there is not a problem of multicollinearity. |
Case 1 continued
Determine the confidence interval CI for variable “Home size”. Make a conclusion about significance of β1.Question 15 options:
| At 95 % of confidence β1 is less than 4.86 but more than 2.81. β1 is not zero, β1 is significant, the variable Home Size and Sales Price are related. | |
| At 95 % of confidence β1 is less than 40.913 but more than 17.78. β1 is not zero, the variable Home Size and Sales Price are related. | |
| At 95 % of confidence β1 is less than 6.15 but more than 5.07.So β1 is not zero. It means β1 is significant and the variable Home Size and Sales Price are related. | |
| At 95 % of confidence β1 is less than 6.15 but more than 5.07. So β1 is zero. It means β1 is not significant and the variable Home Size and Sales Price are not related. |
Case 2
AlwaysGreen is a chain of 27 franchise stores in the nation. A study conducted this year intended to identify the variables that affect Sales. The Excel results presented below estimate Annual Sales (in $ thousands). Assume α =.05.
| SUMMARY OUTPUT | ||
| Regression Statistics | ||
| Multiple R | 0.996583914 | |
| R Square | 0.993179497 | |
| Adjusted R Square | 0.991555568 | |
| Standard Error | 17.64924165 | |
| Observations | 27 | |
| ANOVA | ||
| df | SS | |
| Regression | 5 | 952538.9415 |
| Residual | 21 | 6541.410344 |
| Total | 26 | 959080.3519 |
| Coefficients | Standard Error | |
| Intercept | -18.85941416 | 30.15022791 |
| Number Sq.Ft. (th) | 16.20157356 | 3.544437306 |
| Inventory ($ th) | 0.174635154 | 0.057606068 |
| Amount Spent on Advertising ($ th) | 11.52626903 | 2.5321033 |
| Size of Sales District (th families) | 13.5803129 | 1.770456609 |
| Number of Competing Stores in District | -5.31097141 | 1.70542654 |
Conduct the hypotheses for overall significance of the model
Hypotheses are:Question 16 options:
| Ho: β1=0 Ha: : β1 is not equal to 0Reject Ho if p-value≤α | |
| Ho: β1= β2= β3= β4=0 Ha: At least one beta not equal to zeroReject Ho if p-value≤α | |
| Ho: β1= β2= β3= β4= β5=0 Ha: At least one beta not equal to zeroReject Ho if p-value≤α | |
| Ho: β1= β2= β3=0 Ha: At least one beta not equal to zeroReject Ho if p-value≤α |
Case 2 (continued)
Test statistic F isQuestion 17 options:
| 12.456 | |
| 611.590 | |
| 611.0234 | |
| 23.48 |
Case 2 (continued)
Conduct F test (use the solution in the problem 6) and interpret the overall significance of the model. Use α = .05.Question 18 options:
| p-value is 5.397E-22Conclusion:Since p-value < α -> Reject Ho. At least one independent variable has a relationship with Annual Sales at 95% confidence. | |
| p-value is 5.397E-11Conclusion:Since p-value < α -> Reject Ho. “At least one independent variable has a relationship with Annual Sales” | |
| p-value is 5.397E-22Conclusion:Since p-value < α -> Reject Ho. “All independent variables have a relationship with Annual Sales” | |
| p-value is 5.397E-11Since p-value < α -> Reject Ho. “All independent variables have a relationship with Annual Sales” |
Case 2 (continued)
Conduct t (individual significance) test to determine if ‘Inventory’ has a relationship with ‘Annual Sales’.
t test isQuestion 19 options:
| 3.341 | |
| 1.245 | |
| 3.017 | |
| 1.236 |
Case 2 (continued)
Conduct t (individual significance)test to determine if ‘Inventory’ has a linear relationship with ‘Annual Sales’. Use α = .05.
p-value and conclusion must beQuestion 20 options:
| p-value is .006Model is significant | |
| p-value is .006conclusion isSince p-value (.006) < α (.05) ->Don’t Reject Ho. “Inventory and Annual Salesare not related” | |
| p-value is .0121conclusion isSince p-value (.0121) >α (.05) ->Don’t Reject Ho. “Inventory and Annual Salesare not related” | |
| p-value is .006conclusion isSince p-value (.006) < α (.05) -> At 95 % confidence there is a relationship between Inventory and Annual Sales |
Case 1
The following information regarding a
dependent variable Y and an independent
variable X is provided.
EX = 16 E(X-3) (Y -7)
=-8
EX = 28
E(X-I)7=8
n = 4
SST = 42
SSE = 34Question 1 options:
| Refer to case 1. The slope of the regression function is0.1 | |
| Refer to case 1. The slope of the regression function is11 | |
| Refer to case 1. The slope of the regression function is1 | |
| Refer to case 1. The slope of the regression function is-1 |
Refer to Case 1. The Y intercept isQuestion 2 options:
| 0.1 | |
| 1 | |
| 11 | |
| -1 |
Refer to Case 1. The coefficient of determination isQuestion 3 options:
| -0.1905 | |
| 0.1905 | |
| 0.4364 | |
| -0.4364 |
Refer to Case 1. The coefficient of correlation isQuestion 4 options:
| 0.1905 | |
| -0.1905 | |
| 0.4364 | |
| -0.4364 |
Refer to Case 1. The MSE isQuestion 5 options:
| 17 | |
| 8 | |
| 34 | |
| 42 |
Refer to Case 1. The point estimate of Y when X = 3 isQuestion 6 options:
| 11 | |
| 14 | |
| 8 | |
| 0 |
The following data represent the number of flash drives sold per day at a local computer shop and their prices.
| Price (x) | Units Sold (y) |
| 34 | 3 |
| 36 | 4 |
| 32 | 6 |
| 35 | 5 |
| 30 | 9 |
| 38 | 2 |
| 40 | 1 |
| Refer | to Case 2 data use Excel, Data Analysis, Regression tools and develop a least-squares regression line and explain what the slope of the line indicates. |
Question 7 options:
| y-esimated = 29.7857 – 0.7286xThe slope indicates that as the price goes up by $1, the number of units sold goes up by 0.7286 units. | |
| y-estimated = 29.7857 + 0.7286x. The slope indicates that as the price goes up by $1, the number of units sold goes down by 0.7286 units. | |
| y-esimated = 29.7857 – 0.7286xThe slope indicates that as the price goes up by $1, the number of units sold goes down by 0.7286 units. | |
| None of these alternatives is correct |
Refer to Case 2 data use Excel, Data Analysis, Regression tools and find the coefficient of determination and comment on the strength of relationship between x and y.Question 8 options:
| r 2 = .8556; the estimated regression equation explained 85.56% of the variability in y . Good fit. | |
| r 2 = -.8556; the estimated regression equation explained 85.56% of the variability in y . Good fit. | |
| r2 =-0.92; the estimated regression equation explained 92% of the variability in y . Good fit. | |
| r2 =0.76; the estimated regression equation explained 76% of the variability in y . Good fit. |
Refer to Case 2 data Perform an F test and determine if the price and the number of flash drives sold are related.
Let alpha = 0.01.Question 9 options:
| F = 29.624 < 36.26; p-value = .0028; reject Ho,x and y are related | |
| F = 29.624 > 16.26; p-value = .0028<alpha; reject Ho, x and y are related | |
| F = 29.624 > 16.26; p-value = .0028 > alpha; don’t reject Ho, x and y are not related | |
| None of these alternatives is correct |
Refer to Case 2 perform a t test and determine if the price and the number of flash drives sold are related. Let alpha = 0.01Question 10 options:
| t = -5.4428 p-value = .28; don’t reject Ho, x and y are not related | |
| t = 5.4428 p-value = -.0028; reject Ho, x and y are related | |
| t = -5.4428 p-value = .0028; reject Ho, x and y are related | |
| None of these alternatives is correct |
