Question

The simple linear regression of the data on $Sales and number of customers produced the following ANOVA output:

ANOVA
Source	df	SS	MS	F	Significance F
Regression		46833541
Residual
Total		51360495

Complete as much of the ANOVA table as you need to answer the following two questions (Questions 18 and 19):

4. The calculated value of the test statistic used to test the following null and alternative hypotheses

Ho: The overall regression model is not significant

Ha: The overall regression model is significant

would be

1. F = 186.22
2. F = 4.4139
3. F = 2.1009
4. Z = 1.645
5. Z = 2.288

Use this information to answer the next question:

A simple linear regression was developed with the number of customers as the independent variable and the $Sales as the dependent variable. The following results were obtained:

	Coefficients	Standard Error	t Stat
Intercept	2423	480.96
Customers	8.7	0.64

5. For a week having 750 customers the point estimate for the $ value of Sales predicted by the simple linear regression equation would be (that is, predict $Sales for Customers = 750)

1. $750
2. $6525
3. $2332
4. $8948

Answer 1

The ANOVA uses a F-statistic. Therefore we can discard the last two options of 'Z'.

Here we have the ANOVA output as

ANOVA	k = no. of variables (x and y)
Source	df	SS	MS (SS /df)	F
Regression	1 (k - 1)	46833541	46833541	a. F = 186.22
Residual	18  (explained below)	4526954 (SS Total - SS Reg)	251497.444
Total	19 (n -1)	51360495

Now F-stat = MS Reg / MS Resi

Therefore MS resi = MS reg / F-stat

MS resi = SS resi / df resi

df resi = SS resi / MS resi .............where SS Resi is found in the table above.

So we find the df column first with difference F-stat

F-stat	MS Resi	df Resi
186.22	251495.763	18
4.4139	10610467.2	0
2.1009	22292132.4	0

Since the df can't be '0'. The df = 18.and n = 20

Therefore

F = 186.22

Regression equation for sales predicted by customers is given by

(intercept + slope x)

Pred Sales = 2423 + 8.7 * Cust

Here we use the coefficients col

Customers = 750

Sub x = 750 in reg equation

Pred Sales = 2423 + 8.7 * 750

Sale = $8948