Taking a test i don’t know anything about please help In an Economics course, the correlation between the students' total score prior to the final exam and
their final exam score is r = 0.60. The pre-exam totals for all students in the course have mean 280
points and standard deviation 30 points. The final exam scores have mean 75 points and standard
deviation 8 points.
4. Find the equation of the least-squares regression line for predicting a final exam score from a
student's pre-exam total.
5.
Interpret the slope in context.
6.
Interpret the y-intercept in context.
7.
Calculate the fraction of variability, R?.
8.
Interpret R? in context.

See below for answers and explanations

Step-by-step explanation:

Problem 4:

The line of regression is where:

We are given that , , , , and , therefore our slope, , is:

Therefore, the slope of the regression line is 0.16, which can be used along with the values of and to find the constant :

This means our final regression line is

Problem 5:

The slope, , means that for every 1 point earned for a student's pre-exam total, their final exam score will increase by 0.16 points for each point they earned on the pre-exam.

Problem 6:

The y-intercept (or constant), , means that if a student's pre-exam total were 0, then they would expect to get a 30.2 on the final exam.

Problem 7:

Problem 8:

The fraction of variability (aka. coefficient of determination), , means that a certain proportion (or percentage) of the variance in the response variable can be explained by the explanatory variable. In context, this means that 36% of the variance in final exam scores can be explained by the pre-exam scores.

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step-by-step explanation: