The response variable is Time and the regressor variables are Dist and Cases. Th
ID: 3294663 • Letter: T
Question
The response variable is Time and the regressor variables are Dist and Cases. The results for two regression models are provided: the first has one predictor (Dist) and both are included in the second model. What is the Extra SS for Cases in a model that already contains Dist? Is Cases significant in the second model? (Use statistical test). SET UP the 95% Confidence interval for 2 in second model for Cases. Complete the table below by computing the predicted delivery time and residuals using the material from the Minitab sheet.
Minitab Output
Regression Analysis: Time versus Dist
The regression equation is
Time = 4.96 + 0.0426 Dist
Predictor Coef SE Coef T P
Constant 4.961 2.337 2.12 0.045
Dist 0.042569 0.004506 9.45 0.000
S = 7.17906 R-Sq = 79.5% R-Sq(adj) = 78.6%
Analysis of Variance
Source DF SS MS F P
Regression 1 4599.1 4599.1 89.24 0.000
Residual Error 23 185.4 51.5
Total 24 5784.5
Regression Analysis: Time versus Dist, Cases
The regression equation is
Time = 2.34 + 0.0144 Dist + 1.62 Cases
Predictor Coef SE Coef T P
Constant 2.341 1.097 2.13 0.044
Dist 0.014385 0.003613 3.98 0.001
Cases 1.6159 0.1707 9.46 0.000
S = 3.25947 R-Sq = 96.0% R-Sq(adj) = 95.6%
Analysis of Variance
Source DF SS MS F P
Regression 2 5550.8 2775.4 261.24 0.000
Residual Error 22 233.7
Total 24 5784.5
Dist (ft) Cases Time (min) Predicted (min) Residual 776 10 29.00 1460 30 79.24Explanation / Answer
The SS for second model that contains Cases is 5550.8, and the SS for first model that doesnot contain Cases is 4599.1. Thus, the extra SS is 951.7 (5550.8-4599.1). The p value corresponding to t statistic (t=9.46) of variable Cases is0.000. Declare a variable significant, if the p value is less than alpha=0.05. Thus, Cases is significant in the second model. The 95% confidence interval for beta2 (Cases) is as follows:
betai hat+-talpha/2,n-k-1 SBi, where betai hat is coefficient of betai, talpha/2,n-k-1 is the t critical at alpha/2 and df-n-k-1, SBi is the standard error of the coeffciient betai.
=1.6159+-2.074 (0.1707) [t critical at 0.025 and 22 df is 2.074]
=(1.262,1.970)
Substitute the values for given distance and cases in the regression equation Time=2.34+0.0144 Dist+1.62 Cases
Predicted time=29.7144 Residual: 29-29.7144=-0.7144
Predicted time=71.964 Residual: 79.24-71.964=7.276
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