Question

Suppose you were presented with the following prediction regression equation: Y= 30,000 + 2,000 (X) where the dependent variable is annual salary and the independent variable is years on the job. Interpret the value of the y-intercept (i.e., constant) and the value of the slope.

Suppose you were presented with the following prediction regression equation: Yhat = 30,000 + 2,000 (X) where the dependent variable is annual salary and the independent variable is years on the job. If an individual was on the job 10 years, how much would you predict his or her annual salary to be?

Suppose you were presented with the following prediction regression equation: Yhat = 30,000 + 2,000 (X) where the dependent variable is annual salary and the independent variable is years on the job.

If the above equation came from a model where R² was .45, what can you say about the accuracy of your prediction? Be as detailed as possible!

Answer 1

Answer # 1)

Equation

Y = 30000 + 2000*X

dependent variable Y = annual salary

independent variable X = years

Slope = 2000

Interpretation of slope: with one unit increase in years, the annual salary increases by 2000 times. They both share a positive relation, as year increases annual salary also increases

Intercept = 30000

This implies that even if the year value is 0 , that is for a fresher or new joinee the minimum annual salary paid is 30000

.

Answer# 2)

For the same equation as above , if experience is 10 years , this implies x = 10

we get

Y = 30000+2000*x

y = 30000+2000*10

y = 30000+20000

y = 50000

Hence the predicted annual salary after 10 years would be equal to 50000

.

Answer # 3)

For the same equation as above , it gives R2 = 0.45

R2 is called R square or coefficient of determination

it tells about the percent of variation in the dependent variable explained by the regression model

this model has R2 = 0.45 ~ 45% ( multiply it by 100 , to express it as percent)

this implies the model is able to explain only 45% of the variation in the annual salary

thus there might be other important factors as well which are not covered in this model and they may help predict the annual salary better if incorporated in the model ( like education level of employees)