hi I'm having trouble with these multiple choice questions on multiple linear regression. any help would be
Question:
hi I'm having trouble with these multiple choice questions on multiple linear regression. any help would be great. thank you.
11.
| Sales $m | Wages | No. Staff | Age | Gross Profit | Adv. | Competitors | |
| Sales $m | 1 | ||||||
| Wages $m | 0.81251 | 1 | |||||
| No. Staff | 0.73682 | 0.9249 | 1 | ||||
| Age | -0.11822 | -0.0648 | -0.0329 | 1 | |||
| Gross Profit | 0.07202 | 0.0786 | 0.0013 | -0.0800 | 1 | ||
| Advertising | 0.84222 | 0.7959 | 0.7397 | -0.0143 | 0.0398 | 1 | |
| Competitors | -0.52445 | -0.4472 | -0.3608 | 0.0171 | -0.4493 | -0.39972 | 1 |
The senior Data analyst at osmidium is interested in producing a multi-regression model in order to establish the relationship between SALES (dependent variable) and various explanatory variables. In order to avoid the problem of multicollinearity he constructs the correlation matrix shown above.
Based on the above correlation matrix, displaying respective correlation coefficient combinations, which pair of independent variables are most highly correlated?
a. Wages and No. Staff.
b. Age and Sales
c. Advertising and Age
d. Sales and Advertising
| SUMMARY OUTPUT DEPENDENT VARIABLE = SALES ($m) | |||||
| Regression Statistics | |||||
| Multiple R | 0.9200 | ||||
| R Square | 0.8464 | ||||
| Adjusted R Square | 0.8400 | ||||
| Standard Error | 1.4284 | ||||
| Observations | 150 | ||||
| ANOVA | |||||
| df | SS | MS | F | Significance F | |
| Regression | 6 | 1608.2879 | 268.048 | 131.3807 | 0.0000 |
| Residual | 143 | 291.7540 | 2.04024 | ||
| Total | 149 | 1900.0419 | |||
| Coefficients | Standard Error | t Stat | P-value | ||
| Intercept | 1.1009 | 0.8577 | 1.2836 | 0.2014 | |
| Hrs-Trading (X1) | 0.0178 | 0.0074 | 2.4114 | 0.0172 | |
| Competitors (X2) | -0.4521 | 0.1038 | -4.3539 | 0.0000 | |
| Mng-Exp (X3) | 0.1754 | 0.0329 | 5.3350 | 0.0000 | |
| Sunday (X4) | 0.7224 | 0.2756 | 2.6213 | 0.0097 | |
| Wages $m (X5) | 2.0544 | 0.3542 | 5.8008 | 0.0000 | |
| Advt.$'000 (X6) | 0.0203 | 0.0030 | 6.7480 | 0.0000 |
12. Based on the regression output above, the model is overall significant (useful) because:
a. The number of observations is 150, which is quite large.
b. The intercept coefficient is non-zero.
c. All the 6 slope coefficients are non-zero.
d. The F-test (ANOVA) gives a very low p-value of 0.000.
13. Based on the regression output above,which of the following statements is correct with regard to determining the significance of any variables in the model.
a. Competitors are insignificant in the model because the coefficient is negative.
b. Hrs Trading is insignificant in the model because it has a low p-value of0.0172
c. Sunday is significant in the model because its p-value is less than 0.05
d. None of the variables currently in the model are significant predictors of Sales
14. Based on the regression output above, the equation of the multiple regression model is:
a. = 1.1009 +0.0178X1 - 0.4521X2 + 0.1754X3 + 0.7224X4 + 2.0544X5 + 0.0203X6
b. = 0.9200 + 1.009X1 - 0.8462X2 + 0.1754X3 + 0.7224X4 + 2.0544X5 + 0.0203X6
c. = 1.4284 +0.0178X1 - 0.4521X2 + 0.1754X3 + 0.7224X4 + 2.0544X5 + 0.0203X6
d. =0.0178X1- 0.4521X2 + 0.1754X3 + 0.7224X4 + 2.0544X5 + 0.0203X6+0.8400
15.Based on the regression output above the variable X4 (Sunday)is acoded variable that can only take 2 values. If the store trades on Sunday then X4 = 1 and if not then X4 = 0. Such a variable can be described as being a:
a. Numerical variable
b. Continuous variable
c. Dummy variable
d. Parametric variable
16 . Based on the regression output above, the variable competitors is best described as being:
a. Discrete
b. Continuous
c. Categorical
d. Interval
17.Based on the regression output above, the variable Hrs-Trading is best described as being:
a. Numerical measured on the ratio scale
b. Numerical measured on the interval scale
c. Categorical measured on the ordinal scale.
d. Categorical measured on the nominal scale.
18. Based on the regression output above, the best interpretation for slope coefficientfor Competitors (-0.4521)is:
a. On average, everything else being equal, an extra competitor means a $452,000 decrease in Sales.
b. On average, everything else being equal, an extra competitor means a $452,000 increase in Sales.
c. On average, an extra competitor will not result in any change in Sales.
d.Increasing the number of competitors will not change the amount of Sales.
19.Consider the regression model described by the output shown above. The model currently includes 6explanatory variables. Including a 7th explanatory variable would:
a. Only increase the R -Square value if the variable was a significant predictor of Sales
b. Increase R- Square value even if the variable was not a significant predictor of Sales
c. Would decrease the R -Square vaue regardless of its significance in increasing the power of the model.
d. Would increase the adjusted R-Square value only if the variable was not a significant predictor of sales.
20.Based on the regression model described by the output shown above. The best interpretation of the R Square value (0.8464) would be:
a. 84.64% of the variation in Sales can be explained by the joint variation in the 6 explanatory variables
b. 15.36% of the variation in Sales would be explained by by the joint variation in the 6 explanatory variables.
c.84.64% of the variation in Sales can be explained by other variables not included in the model
d. 84.64% of the variation in sales is caused by the variation in the 6 explanatory variables.
Expert Answer:
