Answer:
(C) The slope of the regression equation is not significantly different from zero
Step-by-step explanation:
Let's suppose that we have the following linear model:
Where Y is the dependent variable and X the independent variable. represent the intercept and
the slope.
In order to estimate the coefficients we can use least squares estimation.
If we are interested in analyze if we have a significant relationship between the dependent and the independent variable we can use the following system of hypothesis:
Null Hypothesis:
Alternative hypothesis:
Or in other wouds we want to check is our slope is significant.
In order to conduct this test we are assuming the following conditions:
a) We have linear relationship between Y and X
b) We have the same probability distribution for the variable Y with the same deviation for each value of the independent variable
c) We assume that the Y values are independent and the distribution of Y is normal
The significance level is provided and on this case is
The standard error for the slope is given by this formula:
Th degrees of freedom for a linear regression is given by since we need to estimate the value for the slope and the intercept.
In order to test the hypothesis the statistic is given by:
The confidence interval for the slope would be given by this formula:
And using the last formula we got that the confidence interval for the slope coefficient is given by:
IF we analyze the confidence interval contains the value 0. So we can conclude that we don't have a significant effect of the slope on this case at 5% of significance. And the best option would be:
(C) The slope of the regression equation is not significantly different from zero