Question

Professor wonders whether a student's homework average (X) could be used to predict their final grade in the course (Y) . She calculates a least-squares regression line, based on data from randomly selected students, and gets Y=21.839+0.724X. Please use this information to answer the following questions.
Which is the dependent variable, and why?

Based on the material taught in this course, which of the following is the most appropriate alternative hypothesis to use for resolving this question?

μ1≠μ2

μd≠0

β1≠0

p1≠p2

At least one of the means is different from at least one of the others.

A student's final course grade is not independent of their homework average.

A student's final course grade is independent of their homework average.

Answer 1

Answer:

The dependent variable is the final grade in the course and is the vriable of interest on this case.

H0: $\beta_1 = 0$

H1: $\beta_1 \neq 0$

And if we reject the null hypothesis we can conclude that we have a significant relationship between the two variables analyzed.

Step-by-step explanation:

On this case w ehave the following linear model:

$Y= 21.839 +0.724 X$

Where Y represent the final grade in the course and X the student's homework average. For this linear model the slope is given by $\beta_1 = 0.724$ and the intercept is $\beta_0 = 21.839$

Which is the dependent variable, and why?

The dependent variable is the final grade in the course and is the vriable of interest on this case.

Based on the material taught in this course, which of the following is the most appropriate alternative hypothesis to use for resolving this question?

Since we conduct a regression the hypothesis of interest are:

H0: $\beta_1 = 0$

H1: $\beta_1 \neq 0$

And if we reject the null hypothesis we can conclude that we have a significant relationship between the two variables analyzed.