Chapter 9, Section 1, Exercise 006 Computer output for fitting a simple linear model is given...

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 this model and give the null and alternative hypotheses for 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 Y⁢=83.2-0.0133X.

Predictor	Coef	SE Coef	T	P
Constant	83.23	11.94	6.97	0.000
X	-0.01327	0.01106	-1.20	0.245

Sample slope:

p-value:

Solutions

Expert Solution

As per the given information,

The regression equation is Y=83.23 - 0.0133X.

Predictor	Coef	SE Coef	T	P
Constant	83.23	11.94	6.97	0.000
X	-0.01327	0.01106	-1.20	0.245

The significance level is 0.05.

Sample slope: - From the above output, the slope coefficient is – 0.01327 which is approximately equals to - 0.0133.

The researcher wants to test if the slope in the population is different from zerot.

The null and the alternative hypothesis is,

p-value: From the above output, the p-value is 0.245.

Since the p-value (0.245) is greater than the significance level 0.05, so the researcher rejects the null hypothesis.

Therefore, it can be concluded that there is not sufficient evidence to support that the slope in the population is different from zero. Thus, the result of the study is statistically insignificant; that is, the model is not statistically effective.

orchestra answered 1 year ago

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