Sample Question for Simple Regression Analysis A result of regression analysis w

Question

Sample Question for Simple Regression Analysis A result of regression analysis where Y represents math SAT score and X represents annual family income was presented as below: y, - 432.4138+0.0013x, se = (16.9061) t=(25.5774) (0.000245) (5.4354) r= 0.7849 pvalue = (5.85x10) (0.0006) df= (1) Interpret the predicted beta coefficients The slope coefficient of 0.0013 means that, if annual family income goes by a dollar, the average math SAT score goes up by about 0.0013 points. The intercept value of 432.4138 means that if family income is zero, the mean (average) math score will be about 432.4138. Very often such an interpretation has no economic meaning. It is best to interpret the intercept term as the average effect on Y of all the variables omitted from the regression model.

Explanation / Answer

We will take null hypothesis

H0=coefficient of x=0

Alternative hypothesis

Ha= coefficient of x not equal to zero

We fail to reject the null hypothesis if

P-value(calculated)< 0.05 at 5% level of significant.

0.0006<.05, we fail to reject the null hypothesis.

Interpret the cofficient of income is correct in given answer that is if average income goes by 1$ then Sat score increases by 0.0013 unit.

The intercept has no economic meaning.

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