You Explain It! Study Time and Exam Scores
After the fir...

Question

You Explain It! Study Time and Exam Scores

After the first exam in a statistics course, Professor Katula surveyed 14 randomly selected students to determine the relation between the amount of time they spent studying for the exam and exam score. She found that a linear relation exists between the two variables. The least-squares regression line that describes this relation is:

ŷ = 6.3333x + 53.0298

b. Interpret the slope.

Accepted Answer

Welcome back, everyone. In this problem, a researcher studying the relationship between hours spent practicing piano and performance score on a music exam found the regression line Y equals 8.25 X plus 62.5. Interpret the meaning of a slope. A says it means that for each additional order of practice, the predicted score increases by 62.5 points. B says for each additional order of practice, the predicted score decreases by 62.5 points. C says for each additional order of practice, the predicted score increases by 8.25 points, and the D says for each additional order of practice, the predicted score decreases by 62.5 points. Now let's make sure we understand exactly what each of these variables and constants mean in this equation. Now, here, we know that Y, based on our problem statement is the predicted performance score, OK? This is the dependent variable. Knowing the next part of our problem or the next part of the equation, X represents the Oers, OK? The Oers spent practicing piano. Because we're told that this researcher studies the relationship between Oers practicing the piano and the performance score on the music exam. Now notice it's Y equals 8.25 X. and 8.25 represents the slope. OK, off the regression line. And now finally 62.5 is a constant, and that represents it's the Y intercept. In other words, if X equals 0, if no hours were spent practicing the piano, then the performance score would be 62.5. So this Y intercept represents the score when no hours are spent practicing. So now if we visualize this, what we're saying is that based on all the data points that our researcher had plot, the line would probably look something like this, OK? And here it intersects the intercepts the Y axis at 62.5. And because it has a slope of 8.25, that means it is increasing by 8.25 on or Y axis for every increase of 1 on or X axis, OK? Because remember, the slope for a straight line is equal to the change in Y or the rise. Divided by the change in X or the run. So, 8.25 is the slope of the regression line. Thus, it represents the change in the predicted performance score for each one unit increase in the number of hours spent practicing. So what that means then is that for every additional hour spent practicing the piano, the performance score would increase by 8.25 points because it is going up by 8.25 each time. In other words, as a student practices more, their predicted performance score improves by 8.25 points for each extra hour of practice. If we look back at our answer choices, that means C is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

Key Concepts

Least-Squares Regression Line

Slope of the Regression Line

Interpretation of Regression Coefficients

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