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End of Section Problem 14.1 (Essay) Use the following data to develop a quadratic model to...

End of Section Problem 14.1 (Essay)

Use the following data to develop a quadratic model to predict y from x. Develop a simple regression model from the data and compare the results of the two models. Does the quadratic model seem to provide any better predictability? Why or why not?

x y x y
14 200 15 247
9 74 8 82
6 29 5 21
21 456 10 94
17 320
Math   Statistics-And-Probability   
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Answer #1

simple

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.985100338
R Square 0.970422677
Adjusted R Square 0.966197345
Standard Error 27.26526302
Observations 9
ANOVA
df SS MS F Significance F
Regression 1 170733.7936 170733.7936 229.6677983 1.31023E-06
Residual 7 5203.761973 743.3945676
Total 8 175937.5556
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept -147.269636 22.77583041 -6.466049026 0.000344996 -201.1259169 -93.41335509
x 27.12787356 1.790052214 15.15479456 1.31023E-06 22.89507269 31.36067444

quadratic

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.997418275
R Square 0.994843215
Adjusted R Square 0.993124286
Standard Error 12.29683009
Observations 9
ANOVA
df SS MS F Significance F
Regression 2 175030.2834 87515.14169 578.757798 1.37131E-07
Residual 6 907.2721818 151.2120303
Total 8 175937.5556
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept -22.01123636 25.64570955 -0.85828143 0.423691879 -84.76402698 40.74155426
x 3.384864819 4.526796386 0.747739578 0.482883408 -7.691806904 14.46153654
x^2 0.937330351 0.175844569 5.330448108 0.001777382 0.507054191 1.367606511

R^2 for linear = 0.970422677

R^2 for quadratic model = 0.994843215


since R^2 for quadratic is more that R^2 for linear
Quadratic model is better

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