Question

Suppose that you fitted the model

E(y) = β₀ + β₁x + β₂x²

to

n = 20

data points and obtained the following MINITAB printout.

Regression Analysis: y versus x, x-sq

Analysis of Variance
Source	DF	Adj SS	Adj MS	F-Value	P-Value
Regression	2	41225.4	20612.7	987.09	0.000
Error	17	355.0	20.9
Total	19	41580.4

Model Summary

S	R-Sq	R-Sq(adj)
4.56972	99.15%	99.05%

Coefficients

Term	Coef	SE Coef	T-Value	P-Value
Constant	12.53	3.40	3.69	0.002
x	9.74	1.49	6.54	0.000
x-sq	-2.339	0.138	-16.95	0.000
Regression Equation
y = 12.53 + 9.74 x − 2.339 x-sq

Do the data provide sufficient evidence to indicate curvature in the relationship between y and x? (Use the exact values found in the MINITAB output. Use α = 0.05.)

State the null and alternative hypotheses.

Find the test statistic.

t =

Find the approximate p-value for the test.

p-value < 0.0100.010 < p-value < 0.020    0.020 < p-value < 0.0500.050 < p-value < 0.1000.100 < p-value < 0.200p-value > 0.200

State your conclusion.

Answer 1

>> Null hypothesis, H​​​​​​0: β​​​​​​2 = 0

Alternative hypothesis, H​​​​​​1: β​​​​​​​​​​​​2 ≠ 0

>> Test statistic, t = -16.95

>> p-value < 0.010

>> Conclusion: Since, the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that the data provide sufficient evidence to indicate curvature in the relationship between y and x.