Question

Researchers are conducting a study in an attempt to establish a linear relationship between the number of online music video views and the number of guitar sales. A computer output for regression is shown and is based on a sample of seven observations.

Predictor Coeff St. Dev t Ratio p-Value
Constant 7.85671094 1.316226455 5.969118 0.001889
Music Video Views 0.094781123 0.027926367 3.393965 0.019378

What represents the 99% confidence interval for the slope of the regression line?

Answer 1

`0.094781123 - 4.032* 0.027926367 =-0.0178180`

`0.094781123 + 4.032* 0.027926367 =-0.2073802`

Explanation:

For this case we have the following output:

Predictor Coeff St. Dev t Ratio p-Value

Constant 7.85671094 1.316226455 5.969118 0.001889

Music Video Views 0.094781123 0.027926367 3.393965 0.019378

For this case the slope of the regression we have:

`\hat b = 0.094781123`

We assume that the standard error is:

`SE_b = 0.027926367`

The confidence interval would be given by:

`\hat b \pm t_(n-2) SE_b`

The degrees of freedom are given by:

`df= 7-2=5`

And the critical value using a significance level of
`\alpha=0.01` is:

`t_(\alpha/2) = 4.032`

And replacing we got;

`0.094781123 - 4.032* 0.027926367 =-0.0178180`

`0.094781123 + 4.032* 0.027926367 =-0.2073802`