Q1) Consider the following data points shown in the table:
|
xi
|
1
|
2
|
3
|
4
|
5
|
9
|
|
yi
|
2
|
2
|
6
|
8
|
11
|
13
|
a) Create the estimated regression equation by calculating the values of b0 and b1
b) Calculate the coefficient of Determination r2. Comment on goodness of the fit.
c) Using t-test, test the following hypotheses (You have to work out ALL the steps that lead to calculation of t statistic) (a= .05): This is the biggest section you have to demonstrate your work.
H0 : β1 = 0
H0 :β1≠ 0
Super Markets, Inc. is thinking of expanding into Scottsdale, Arizona, area. You as director of planning, should present an analysis of proposed expansion to operating committee of board of directors. As part of your proposal, you require to include information on amount of people in region spend per month for grocery items. You would also like to comprise information on relationship between amount spent for grocery items and income. Your assistance gathered the following sample information. Data is available on data disk supplied with the text.
|
Household
|
Amount Spent
|
Monthly Income
|
|
1
|
555
|
4388
|
|
2
|
489
|
4558
|
|
.
|
.
|
.
|
|
.
|
.
|
.
|
Let amount spent be dependent variable and monthly income independent variable. Construct a scatter diagram, by using a software package.
a) Find out regression equation. Interpret slope value.
b) Find out the coefficient of correlation. Can you conclude that it is greater than 0?