Question

Given here are the data from a dependent variable and two independent variables. The second independent variable is an indicator variable with several categories. Hence, this variable is represented by x₂, x₃, and x₄. How many categories are there for this independent
variable? Use a computer to perform a multiple regression analysis on this data to predict y from the x values. Discuss the output and pay particular attention to the dummy variables.

y	x1	x2	x3	x4
11	1.9	1	0	0
3	1.6	0	1	0
2	2.3	0	1	0
5	2.0	0	0	1
9	1.8	0	0	0
14	1.9	1	0	0
10	2.4	1	0	0
8	2.6	0	0	0
4	2.0	0	1	0
9	1.4	0	0	0
11	1.7	1	0	0
4	2.5	0	0	1
6	1.0	1	0	0
10	1.4	0	0	0
3	1.9	0	1	0
4	2.3	0	1	0
9	2.2	0	0	0
6	1.7	0	0	1

Appendix A Statistical Tables

Number of categories =

.

The regression equation is: y− =

+

x1 +

x2 -

x3 -

x4 (Round answers to 3 decimals.)

Answer 1

Answer:

Given Data

Using Excel complite this question

Output of Multiple regression is

Here number of category is 4

Suppose those category are A = ( 0 ,0,0)

B = (1,0,0)

C = (0,1,0)

D= (0,0,1)

this are the 4 category .

and least square regression equation is

is the regression equation .

If you want to predict first independent variable X1 = 2.2 and second independent varable catedory B=(1,0,0)

then predict Y value using this

= 7.90286 + 1.458051 (1) - 5.88127 (0) - 4.10836 *(0)

= 7.90286 +1.458051

=9.38337

is the predicted value of Y for category B.