If you remember from the last chapter, we created a regression line that allows

Question

If you remember from the last chapter, we created a regression line that allows us to predict a person's value on one variable given his/her value on another variable. The formula is: y = b(x) + a, where "y" is the score you are trying to predict, "b" is the coefficient for the predictor, "x" is the person's actual score on the predictor, and "a" is the constant. Adding predictors just adds more "b(x)" terms in the equation, one for each predictor. Using this information, we are trying to predict test scores based on motivation (on a 1 - 10 pt scale) and number of hours studied. The regression equation looks like this: Predicted exam score = 2.0 (score on motivation) + 8.0(hours studied) + 50 If Emily scored a 4 on the motivation scale and studied for 3 hours, what is her predicted score? For every point increase on the motivation scale, how many points does test score increase? For every hour studied, how many points does test score increase? If somebody scored zero on motivation and studied for zero hours, what is the predicted score?

Explanation / Answer

Regression equation :

Pedicted 'Exam score = 2.0(score on motivation) + 8.0(hours studied) +50

1. If Emily scored a 4 on the motivtion scale and studied for 3 hours, what is her predicted score?

Given,

Score on Motivation =4 ; Hours studied = 3 ;

Substitute these values in the regression equation

Pedicted 'Exam score = 2.0(score on motivation) + 8.0(hours studied) +50

Pedicted 'Exam score = 2.0x4 + 8.0x3 + 50 =8+24+50 = 82

Emily 's Pedicted 'Exam score =82

2. For every point increase on the motivtion scale, how many points does test score increase.

The test score increses by the coefficient of the score of the motivation ie.2.

Pedicted 'Exam score = 2.0(score on motivation) + 8.0(hours studied) +50 ------------------(1)

increase the score of motivation by 1

Pedicted 'Exam score = 2.0(score on motivation + 1 ) + 8.0(hours studied) +50

Pedicted 'Exam score = 2.0(score on motivation) + 2 + 8.0(hours studied) +50 --------------------(2)

(2) -(1) =2

For every point increase on the motivation scale, test score increases by 2 points

3. For every hour studied, how many points does test score increase?

The test score increses by the coefficient of the hours studied ie.8

Pedicted 'Exam score = 2.0(score on motivation) + 8.0(hours studied) +50 ------------------(1)

increase the hours studied by 1

Pedicted 'Exam score = 2.0(score on motivation ) + 8.0(hours studied+1) +50

Pedicted 'Exam score = 2.0(score on motivation) + 8.0(hours studied) +8 +50 --------------------(2)

(2) -(1) =8

For every studied test score increases by 8 points

4. If somebody scored zero on motivation and studied for zero hours, what is predicted score.

Score on motivation = 0 ; Hours studied = 0;

Substitute these values in the regression equation

Pedicted 'Exam score = 2.0(score on motivation) + 8.0(hours studied) +50

Pedicted 'Exam score = 2.0x0 + 8.0x0+50=0+0+50 = 50

Predicted score =50

If somebody scored zeo on motivtion and studied for zero hours, the predicted score = 50

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