Question

Chapter 9, Section 1, Exercise 006 Computer output for fitting a simple linear model is given below. State the value of the sample slope for the given model. In testing if the slope in the population is different from zero, identify the p-value and use it (and a 5 % significance level) to make a clear conclusion about the effectiveness of the model. The regression equation is Upper Y ⁢ equals 84.8 minus 0.0137 Upper X Predictor Coef SE Coef T P Constant 84.78 12.16 6.97 0.000 Upper X -0.01374 0.01145 -1.20 0.245 Sample slope: p-value: Is the model effective?

Answer 1

Solution:

   We are given that:

Regression model :

Predictor	Coef	SECoef	T	P
Constant	84.78	12.16	6.97	0.000
X	-0.01374	0.01145	-1.2	0.245

Level of Significance = 5% = 0.05

We have to test if the slope in the population is different from 0 or not.

Thus we state null hypothesis H0 and alternative hypothesis H1 as:

H0: Regression model is not effective or

Vs

H1: Regression model is effective or

Thus from given output:

Sample Slope = Coefficient of X variable = -0.01374

P-value = P-value of slope = 0.245

Decision rule: Reject H0 , if P-value < 0.05 level of significance, otherwise we fail to reject H0.

Since P-value = 0.245 > 0.05 level of significance, we fail to reject null hypothesis H0, hence we conclude that: regression model obtained from the sample is not effective.