4.5 For the following four regressions, predict the value of the y variable for

Question

4.5 For the following four regressions, predict the value of the y variable for the value of the x variable given. a. wage = 2.05 + 1·32education, where wage is dollars earned per hour and educa- tion is number of years the person went to school. Predict the wage if a person has 15 years of education. b. GPA = 1.14 + 0·23hours study, where GPA is measured in points and hours study is the number of hours spent studying in a week. Predict the GPA for a student who studies 11 hours a week. c. sleep-10.33-044work, where sleep is hours spent sleeping per night and work is the number of hours worked per day. Predict the amount of sleep a person gets a night if they work 7 hours a day.

Explanation / Answer

(a) Given regression equation is as follows –

Wage = 2.05 + 1.32education

Where,

Wage = dollars earned per hour

education = number of years the person went to school

Calculating wage rate if a person has 15 years of education –

Wage = 2.05 + 1.32education

          = 2.05 + 1.32*15

          = 2.05 + 19.8

          = 21.85

Thus, if a person has 15 years of education then as per given regression equation his wage rate will be $21.85 per hour.

(b) Given regression equation is as follows –

GPA = 1.14 + 0.23hours study

Where,

GPA = Grade point average

hours study = number of hours spent studying in a week

Calculating GPA of a student who studies for 11 hours in a week –

GPA = 1.14 + 0.23hours study

         = 1.14 + 0.23 * 11

         = 1.14 + 2.53

         = 3.67

Thus, if a student studies for 11 hours in a week then as per given regression equation his GPA will be 3.67.

(c) Given regression equation is as follows –

Sleep = 10.33 – 0.44work

Where,

Sleep = Hours spent sleeping per night

work = number of hours worked per day

Calculating amount of sleep a person gets at night if he works for 7 hours a day –

Sleep = 10.33 – 0.44work

          = 10.33 – 0.44 * 7

         = 10.33 – 3.08

          = 7.25

Thus, if a person works for 7 hours a day then as per given equation he will sleep for 7.25 hours per day at night.

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