Question

1. Using the following data on candidates for the Virginia state legislature:
   1. Calculate the slope and intercept for the regression line. Write out the equation model. Be sure to show your work.
   2. Interpret the slope and intercept.

Candidate for Virginia General Assembly	X = number of years in state politics	Y = votes received in Albemarle County
Isabelle	18	2300
Benjamin	5	2950
Sophia	12	1780
Jacob	2	3120

Answer 1

Solution:

We are given following data on candidates for the Virginia state legislature.

Candidate for Virginia General Assembly	X = number of years in state politics	Y = votes received in Albemarle County
Isabelle	18	2300
Benjamin	5	2950
Sophia	12	1780
Jacob	2	3120

Part a) Calculate the slope and intercept for the regression line. Write out the equation model. Be sure to show your work.

Y = votes received in Albemarle County depends on X = number of years in state politics, thus Y is response variable( Dependent) and X is Explanatory variable (Independent).

where

Slope is:

and Intercept is:

where

Thus we need to make following table:

Candidate for Virginia General Assembly	X = number of years in state politics	Y = votes received in Albemarle County	X^2	XY
Isabelle	18	2300	324	41400
Benjamin	5	2950	25	14750
Sophia	12	1780	144	21360
Jacob	2	3120	4	6240

Thus

Slope is:

Now find mean of X and Y to get Intercept.

Thus intercept is:

Thus equation of regression line is:

Part b) Interpret the slope and intercept.

We have Slope = and intercept =

Interpretation of Slope:

For one unit increase in number of years in state politics , there is decrease of 65.6089 votes received in Albemarle County.

Interpretation of Intercept:

Intercept is value of response variable Y , when independent variable is 0 or absent.

Here if Candidate do not have any number of years in state politics, then number of votes received in Albemarle County would be 3143.4572 .