Question

Run a regression analysis on the following bivariate set of data with y as the response variable. x y 37.2 26.9 66.2 41.4 80.9 37.6 83.7 45 55 31.2 46.3 29.1 82 44.1 71.6 36.1 54.7 29.3 56.4 33.8 Predict what value (on average) for the response variable will be obtained from a value of 45.1 as the explanatory variable. Use a significance level of α = 0.05 to assess the strength of the linear correlation. What is the predicted response value? (Report answer accurate to one decimal place.)

Answer 1

we have given data ,

x	y
37.2	26.9
80.9	37.6
83.7	45
55	31.2
46.3	29.1
82	44.1
71.6	36.1
54.7	29.3
56.4	33.8

Regression Analysis: y versus x

Analysis of Variance

Source DF Seq SS Contribution Adj SS Adj MS F-Value P-Value
Regression 1 298.33 87.96% 298.33 298.332 51.14 0.000
x 1 298.33 87.96% 298.33 298.332 51.14 0.000
Error 7 40.84 12.04% 40.84 5.834
Total 8 339.17 100.00%

Model Summary

S R-sq R-sq(adj) PRESS R-sq(pred)
2.41532 87.96% 86.24% 71.9728 78.78%

Coefficients

Term Coef SE Coef 95% CI T-Value P-Value VIF
Constant 12.09 3.27 ( 4.35, 19.83) 3.69 0.008
x 0.3598 0.0503 (0.2408, 0.4787) 7.15 0.000 1.00

Regression Equation

y = 12.09 + 0.3598 x

Now ,if x= 45.1 then

y =12.09+0.3598*45.1

y=28.3

So we get predicted response value =28.3

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