For the following four regression equations explain what the slope and intercept
ID: 1190778 • Letter: F
Question
For the following four regression equations explain what the slope and intercept mean. (Shown in picture 4.3 F For the following four regression equations, explain what the slope and intercep mean. a. wage = 2.05 + 1 . 32education, where wage is dollars earned per hour and educa- bGPA = 1.14 + 0.23hours study, where GPA is measured in points and hours c, sleep = 10.33-044work, where sleep is hours spent sleeping per night and d. savings = 586 + 0.1 5salary, where savings is dollars saved in the bank and the tion is number of years the person went to school. study is the number of hours spent studying in a week. work is the number of hours worked per day salary is the number of dollars earned in a year.Explanation / Answer
a- Here the Slope = 1.32 and intercept= 2.05 (constant term)
interpretation of Slope- If Education is increased by one unit then the wage will be increased by 1.32 units.
interpretation of Intercept- If Education is Zero then the wage will be equal to 2.05 approximately.
The interpretation of the intercept doesn’t make sense in the real world. But you can relate it like if there is no educcation (Education =0 ) then there will be no Wage hike and it will be constant = 2.05. (This logic applies to all the Regression equation given below).
b) interpretation of Slope- If Hours study is increased by one unit then the GPA will be increased by 0.23 units.
interpretation of Intercept- If Hours Study is Zero then the GPA will be equal to 1.14 approximately. (Use same logic for Explanation as above)
c)- interpretation of Slope- If Work is increased by one unit then the Sleep will be Decreased by 0.44 units. (here the decrease is because of Negative sign and thus slope is negative means it is inversely proportional and any incerement in Work will decrease the hours of sleep. (It makes sense :)
interpretation of Intercept- If work is Zero then the Sleep will be equal to 10.33 approximately. (Imagine 10.33 hours of sleep :) daily) this Regression equation is good )
d)- interpretation of Slope- If Salary is increased by one unit then the Savings (Dollars in Bank) will be increased by 0.15 dollar in a year.
interpretation of Intercept- If Salary is Zero then the Savings will be equal to 586 dollars approximately. (as i told u in option A) explanation that intercept does not make sense in real world and it is proved in this option , if you dont have salary how could salary be $586. But also it this regression equations depends on what set of observation we have regressed. so yes it can be possible that even after no salary there was savings of $586 , if they have regrresed that set of people who have some initial savings apart from their income.