Discussion question: Statistics in action
1.Please read the case in the attachment to answer what is the case about and describe the key variables by using couple sentences.
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2. Also following is one of my classmate’s post, could you please review and make reflection on her post. Couple sentences will be enough. Also please use the above model to calculate 90% confidence interval for mean cost and 90% prediction interval for cost when DOTEST= 500 thousand dollars, and STATUS=0.
Classmate: First I ran a multiple regression with all the variables and used their P values to narrow down the relevant variables to: STATUS, DOTEST, and DAYSEST. I ran the regression for these three variables and found that the P value for DAYSEST increased from 0.058 to 0.122. If we are using a 95% confidence then the alpha value would be 0.05 and since 0.122 > 0.05 DAYSEST is no longer a relevant variable. This leaves STATUS and DOTEST as the remaining relevant variables. Below is the regression.
The adjusted R-square shows at 97.52% which means that 97.52% change in cost can be explained by the regression model adjusted for sample size and number of variables. (COST = -20.5 + 166.3 STATUS + 0.93078 DOTEST)
The model is useful as determined by the P value of the regression equation (0.000 < 0.05) which is less than our alpha.
Regression Analysis: COST versus DOTEST, STATUSAnalysis of Variance
Source DF Seq SS Contribution Adj SS Adj MS F-Value P-ValueRegression 2 865106382 97.55% 865106382 432553191 4609.61 0.000 STATUS 1 8941884 1.01% 1068912 1068912 11.39 0.001 DOTEST 1 856164498 96.54% 856164498 856164498 9123.92 0.000Error 232 21770257 2.45% 21770257 93837 Lack-of-Fit 231 21769231 2.45% 21769231 94239 91.85 0.083 Pure Error 1 1026 0.00% 1026 1026Total 234 886876639 100.00%
Model Summary S R-sq R-sq(adj) PRESS R-sq(pred)306.329 97.55% 97.52% 23394862 97.36%
CoefficientsTerm Coef SE Coef 95% CI T-Value P-Value VIFConstant -20.5 26.8 ( -64.8, 23.8) -0.77 0.445STATUS 166.3 49.3 ( 85.0, 247.7) 3.38 0.001 1.02DOTEST 0.93078 0.00974 (0.91469, 0.94687) 95.52 0.000 1.02
Regression EquationCOST = -20.5 + 166.3 STATUS + 0.93078 DOTEST
