Question

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 significance level) to make a clear conclusion about the effectiveness of the model.

The regression equation is : Y= 93.9 - 6.86XPredictor Coef SE Coef T PConstant 93.874 4.763 19.71 0.000X -6.8565 0.8001 -8.57 0.000Sample Slope:P Value:Is the model effective?

Answer 1

The answer is "Slope coefficient is significant".

Explanation:

Slope is = - 68565

By each unit, this same value of the response variable reduces by – 6.86 throughout the slope value obtained

Consider zero hypothesis and options

Zero assumptions,
`h_o: \beta = O`

Hypothesis of alternative,
`h_a: \beta \\eq O`

Suppose that now the degree of importance is= 0.05

The p-value of the slope coefficient estimates is =0.000

Compare the p-value and the meaning

That p-value is smaller than the meaning level and rejects the null hypothesis

That's why the slope coefficient value is therefore significant.