om
Sam321
303MTPrep21.pdf
Regression Analysis
r2 0.547 r 0.740
Std. Error 12.2 n 16 k 1
Dep. Var. Car Washes
ANOVA table Source SS df MS F p-value
Regression 2,521.46 1 2,521.46 16.90 .0011 Residual 2,088.47 14 149.18
Total 4,609.94 15
Regression output confidence interval variables coefficients std. error t (df=14) p-value 95% lower 95% upper Intercept 23.6
Rainfall (in) 1.3 0.3142 4.111 .0011 0.6178 1.9654
Observation Car Washes Predicted Residual 1 58.0 70.1 -12.1 2 62.0 64.9 -2.9 3 74.0 73.9 0.1 4 75.0 92.0 -17.0 5 88.0 77.8 10.2 6 86.0 95.9 -9.9 7 105.0 98.5 6.5 8 109.0 94.6 14.4 9 100.0 99.8 0.2
10 120.0 102.3 17.7 11 68.0 85.5 -17.5 12 88.0 88.1 -0.1 13 88.0 70.1 17.9 14 97.0 107.5 -10.5 15 71.0 77.8 -6.8 16 94.0 84.3 9.7
24.4
Residuals by Predicted
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-24.4
-12.2
0.0
12.2
24.4
60 70 80 90 100 110
Re si
du al
(g ri
dl in
es =
s td
. e rr
or )
Predicted
-24.4
-12.2
0.0
12.2
24.4
30 40 50 60 70
Re si
du al
(g ri
dl in
es =
s td
. e rr
or )
Rainfall (in)
Residuals by Rainfall (in)
-5
0
5
10
15
20
Re si
du al
Normal Probability Plot of Residuals
-20
-15
-10
-5
-2.0 -1.0 0.0 1.0 2.0 Normal Score
Rainfall (in) Car Washes 36 58 26 62 39 74 53 75 42 88 56 86 58 105 55 109 59 100 61 120 48 68 50 88 36 88 65 97 42 71 47 94 30 78
Regression Analysis ANOVA table r2 0.547 Source SS df MS F p-value
r 0.740 Regression 2,521.46 1 2,521.46 16.90 .0011
Std. Error 12.2 Residual 2,088.47 14 149.18 n 16 Total 4,609.94 15 k 1
Dep. Var. Car Washes
Regression output confidence interval variables coefficients std. error t (df=14) p-value 95% lower 95% upper Intercept 23.6
Rainfall (in) 1.3 0.3142 4.111 .0011 0.618 1.965
A local entrprenuer is considering investing in a car wash. She has done some research and discovered a potential relationship between rainfall (in mm) and the number of car washes for the region. A bright young student from GMU suggested a regression analysis might help in predicting future activity at the car wash. Help the entreprenuer 1) prepare a model, assess it's goodness, and 3) if appropriate use the model to predict possible number of car washes at 25 mm and at 70 mm of rain. Intertret the model and comment.
