Question

Using R and the data in the table below, perform the regression of D on C (i.e., report the regression equation).

C	D
3	2
6	7
8	5
9	4
1	0
3	4

Hint: The code to enter the vectors C and D into R is:

C <- c(3, 6, 8, 9, 1, 3)

D <- c(2, 7, 5, 4, 0, 4)

You must figure out how to obtain the regression equation from R. Enter the code below and write the regression equation using the output provided by R.

Code:

Regression equation (remember to use a hat when it is appropriate):

Answer 1

Solution: We need to obtain the regression equation of D on C. It would be of the form

Where is the predicted value of the response variable D, C is the given value of the explanatory variable.

Also, b0 is the y-intercept and b1 is the slope of the regression equation. They are given by the following formula--

where are the means of the response and explanatory variables.

The values of b0 and b1 from R-software are obtained as b0 = 1.067 and b1 = 0.520.

So, the regression equation obtained is = 1.067 + 0.520 C

Th code in R-software is:

C <- c(3, 6, 8, 9, 1, 3)

D <- c(2, 7, 5, 4, 0, 4)
lm(D~C)

The output of the code is attached as an image below: