average highway and arterial speeds. Assume all regression assumptions are met.
ID: 356740 • Letter: A
Question
average highway and arterial speeds. Assume all regression assumptions are met. Multiple R R Square Adjusted R Square 0.773657165 Standard Error 6.474064904 0.889127899 0.790548421 ANOVA 5 9808.229632 1961.64592646.802227 8.81035E-20 62 2598.638015 41.91351638 67 12406.86765 Total Coefficients Standard Error t Stat P-value Lower 95% Upper95% Lower 950% Upper 95.0% 139.1041107 16.69063456 8.334261358 1.043E-11 105.7400079 172 4682135 105.7400079 172.4682135 ay MPH 1073471854 0247420454 -4.33865445 5.379E-05 -1.56805829-0578885418 -156805829-0.578885418 2.04836152 0.667165757-3.0702437870.0031727-3.382006852-0.714716188-3.382006852-0.714716188 3.589696886 2.953037124-1.2155949060.2287478-9.492733928 2 313340156-9.492733928 2.313340156 5.009669683 2.103615129 2.3814573370.0203282 0.804602997 9.214736368 0804602997 9.214736368 3.410579515 3.229696038 1.0560063470.2950629-3.045490811 9.866649841-3.045490811 9.866649841 HW Arterial MPH 8. (5 points) Is the regression model and are all variables significant? a. The model and all variables are significant. b. The model is significant, but no variables are. c. The model is not significant, but some variables are. d. The model is not significant, but all variables are. e. Neither model nor variables is significant. f. None of the above/There is not enough information to tell. Explanation 9. (5 points) What is the regression equation? a. Delay 139.1 1.1*HiWay-2.0*Art. -3.6 Small+5.0 Large 3.4 XL b. Delay139.1 1.1*HiWay - 2.0*Art 5.0 Large c. Delay-3.6 Small+3.4 XL d. Delay- 139.1 +5.0 Large 3.4 XL c. None of the above/ Explanation: There is not enough information to tell. Questions continued on the next page!)Explanation / Answer
8.
It is the p-values associated with the variables that determine their significance. The p-values are associated with the null hypothesis which states that the coefficient of the variable is zero, or the variable is insignificant. Any p-value lesser than 0.05 indicates that null hypothesis can be rejected, i.e. the variable is significant and vice versa. Hence, in our case, the variables SMALL and VERY LARGE have p-values more than 0.05 indicating that they are the insignificant ones while the rest are significant.
The f-test tests the null hypothesis that all the independant variables are insignificant. In other words, it determines whether our model is best fitted with the data we have. So, if the f-value is larger than the f-significant value, than we can reject null hypothesis. In other words, the model would be significant. In our case, the f-value (46.80) is far greater than f-significant (8.81E-20). Hence, rejecting the null hypothesis, we can sat that our model is statistically significant.
Thus, our model is significant, but not all the variables are. So the answer to question 8 is (f)
9.
The answer can be both (a) and (b) depending on the requirement of accuracy as well as the number of variables.
An insignificant variable may not be necessarily 0. It is just that the variable might not have sufficient information about the dependant variable. If we want the exact inference, then the coefficient of the variables should not change. Hence we can include SMALL and VERY LARGE in the model, making (a) as the right choice.
Whereas, if we are considering forecasting ,then the insignificant variables can lead to increased variance, which is unnecessary. Hence, we can remove the variables SMALL and VERY LARGE from the equation, making (b) as the right choice.
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