Eighteen data points on M and x are used to estimate the quadratic regression mo

Question

Eighteen data points on M and x are used to estimate the quadratic regression model M = a + bX + cX^2. A new variable, Z, is created to transform the regression into a linear form. The computer output from this regression is What is the variable Z equal to? Write the estimated quadratic relation between M and X. Test each of the three estimated parameters for statistical significance at the 2 percent level of significance. Show how you performed these tests and present the results. Interpret the p-value for c. What is the predicted value of M when X is 300?

Explanation / Answer

a)Z=X^2

b)M=290.063-5.8401X+0.7126X^2

c)We need to check for the t and p values

At 2% level of significance, we reject the parameter if p value>0.02

But we can see that the p values are 0.0001,0.0179,0.0025 and hence all the coefficients are significant.

d)p value for c=0.0025. Which means that there is only .25% chance that the X^2 term would not be significant.

e)M=290.063-5.8401*300+0.07126*300*300=4951.433

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