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# Interpreting computer output for regression

Desiree is interested to see if students who consume more caffeine tend to study more as well. She randomly selects 20 students at her school and records their caffeine intake (mg) and the number of hours spent studying. A scatterplot of the data showed a linear relationship.
This is computer output from a least-squares regression analysis on the data:
PredictorCoefSE CoefTP
Constant2, point, 5440, point, 13418, point, 9550, point, 000
Caffeine (mg)0, point, 1640, point, 0572, point, 8620, point, 005
S, equals, 1, point, 532, start text, R, negative, S, q, end text, equals, 60, point, 032, percent, start text, R, negative, S, q, left parenthesis, a, d, j, right parenthesis, end text, equals, 58, point, 621, percent
Question 1
What is the equation of the least-squares regression line?
PredictorCoefSE CoefTP
Constant2, point, 5440, point, 13418, point, 9550, point, 000
Caffeine (mg)0, point, 1640, point, 0572, point, 8620, point, 005
S, equals, 1, point, 532, start text, R, negative, S, q, end text, equals, 60, point, 032, percent, start text, R, negative, S, q, left parenthesis, a, d, j, right parenthesis, end text, equals, 58, point, 621, percent

Question 2
Which statement about the slope is true?
PredictorCoefSE CoefTP
Constant2, point, 5440, point, 13418, point, 9550, point, 000
Caffeine (mg)0, point, 1640, point, 0572, point, 8620, point, 005
S, equals, 1, point, 532, start text, R, negative, S, q, end text, equals, 60, point, 032, percent, start text, R, negative, S, q, left parenthesis, a, d, j, right parenthesis, end text, equals, 58, point, 621, percent

question 3
Which statement about the y-intercept is true?
PredictorCoefSE CoefTP
Constant2, point, 5440, point, 13418, point, 9550, point, 000
Caffeine (mg)0, point, 1640, point, 0572, point, 8620, point, 005
S, equals, 1, point, 532, start text, R, negative, S, q, end text, equals, 60, point, 032, percent, start text, R, negative, S, q, left parenthesis, a, d, j, right parenthesis, end text, equals, 58, point, 621, percent

question 4
How large is a typical prediction error when using this model to predict study time from caffeine intake?
PredictorCoefSE CoefTP
Constant2, point, 5440, point, 13418, point, 9550, point, 000
Caffeine (mg)0, point, 1640, point, 0572, point, 8620, point, 005
S, equals, 1, point, 532, start text, R, negative, S, q, end text, equals, 60, point, 032, percent, start text, R, negative, S, q, left parenthesis, a, d, j, right parenthesis, end text, equals, 58, point, 621, percent

question 5
About what percentage of the variation in study time can be explained by the regression on caffeine intake?
PredictorCoefSE CoefTP
Constant2, point, 5440, point, 13418, point, 9550, point, 000
Caffeine (mg)0, point, 1640, point, 0572, point, 8620, point, 005
S, equals, 1, point, 532, start text, R, negative, S, q, end text, equals, 60, point, 032, percent, start text, R, negative, S, q, left parenthesis, a, d, j, right parenthesis, end text, equals, 58, point, 621, percent