A study was conducted to examine the time required to complete a construction pr

Question

A study was conducted to examine the time required to complete a construction project The variables in the study were: Y-time to complete the project in days X, = size of the contract in $10,000 x, = number of work-days adversely affected by weather X, = number of subcontractors involved in the project Model Summary S R-sq R-sq(adj) R-sq (pred) 9.42% 14.3163 75.423 6872% coofficients Coef SE Coef T-Value P-Value VI 19.3 Term 11.1 1.740.110 I. What is the predicted value of What is the value of SST? What is the value of MSR? What is the value of S'? What is the predicted value of Y when X,-7.X,-5, and X3 Analysis of Variance 2. DF Adj SS Adj MS F-Value P-Value Source Regression 3 6918.8 2306.311.25 0.001 0.291 .91 0.359 1.23 1 252.3 252.3 1 187.5 187.5 1 2442.6 2442.611.92 0.005 X1 4. X3 Error Total 11 2254.5 205.0 4 9173.3 (round your answer to tvo decimal places) Regression Equation . What is the residual for the predicted value in question 5? (round your 7. If we were conducting the hypothesis test H .-0 vs. H # 0, what would be the calculated value ofthe test statistic? (round your g. What is the lower bound of a 95% confidence interval for (round your answer to two decimal places) 9. What is the upper bound of a 95% confidence interval for ? (round your answer to two decimal places answer to two decimal places) Y =-19.3-0.0835 X1 + 1.14 X2 + 6.40 X3 answer to two decimal places) 0. Multiple choice: Perform a hypothesis test forH = 0 vs. H : , 0 with alpha-0.05. What is your conclusion? a) Reject Ho, there is evidence that X is significant to the model. b) RejectH, there is ot evidence that X is significant to the model. c) Do not rejectH, there is evidence that Xi is significant to the model. d) Do not rejectH, there is not evidence that X is significant to the model. 15 60 12 15 15 12 120 20 21 260

Explanation / Answer

1) from the regression equation we see that the coeffiecient of X2 is 1.14 , hence b2 is 1.14

2) 9173.3 , it is given in the adj SS column of the regression output , it is the sum of regression and error

3) MSR is 205 from the Adj MS column

4) S is given as 14.31 , so S2 is 14.31*14.31 = 204.77

5) based on the regression equation

y = -19.3 -0.0835*x1 +1.14*x2 +6.4*x3
-19.3 -0.0835*7 +1.14*5+6.4*3
=5.015

6) from the data we see that the value of y is 7 for
x1 = 7 , x2 = 5 and x3 = 3
so residual
actual - predicted
7-5.015 = 1.985

Please note that we can answer only 4 subparts of a question at a time , i have answered 6 .

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