Question

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

15 229 15 247 9 74 8 82 6 29 5 21 21 456 10 94 17 320

Answer 1

Answer:-

Given That:-

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?

Given,

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
	0.937330351	0.175844569	5.330448108	0.001777382	0.507054191	1.367606511

for linear = 0.970422677

for quadratic model = 0.994843215

since for quadratic is more that for linear

Quadratic model is better

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