Using a sample of recent university graduates, you estimate a simple linear regression using initial annual salary as the dependent variable and the graduate's weighted average mark (WAM) as the explanatory variable. If the regression model has an estimated intercept of 2200 and an estimated slope coefficient of 550, what is the predicted starting salary of a student with a WAM of 82?

Question

Using a sample of recent university graduates, you estimate a simple linear regression using initial annual salary as the dependent variable and the graduate's weighted average mark (WAM) as the explanatory variable. If the regression model has an estimated intercept of 2200 and an estimated slope coefficient of 550, what is the predicted starting salary of a student with a WAM of 82?

Answer 1

Substitute 82 for x into the equation and solve for y.

Regression equation is predicted y = a + bx
...where a represents the y-intercept and b the slope.

With your data:
y = 2200 + 550(82)

I'll let you take it from here.

Answer 2

To find the predicted starting salary of a student with a WAM of 82, we will use the linear regression model with the estimated intercept and slope coefficients.

The simple linear regression equation is given by:
Y = b0 + b1*X

Where:
Y represents the dependent variable (initial annual salary)
X represents the explanatory variable (WAM)
b0 represents the estimated intercept (2200)
b1 represents the estimated slope coefficient (550)

Now, substitute the values into the equation:
Y = 2200 + 550*X

Plug in the value of X (WAM = 82):
Y = 2200 + 550*82

Multiply:
Y = 2200 + 45100

Add:
Y = 47300

Therefore, the predicted starting salary for a student with a WAM of 82 is $47,300.