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

Answer:

$0.094781123 - 4.032* 0.027926367 =-0.0178180$

$0.094781123 + 4.032* 0.027926367 =-0.2073802$

Step-by-step 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;

$0.094781123 - 4.032* 0.027926367 =-0.0178180$

$0.094781123 + 4.032* 0.027926367 =-0.2073802$