Question
In: Statistics and Probability
The simple linear regression of the data on $Sales and number of customers produced the following...
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):
- 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
- F = 186.22
- F = 4.4139
- F = 2.1009
- Z = 1.645
- 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 |
- 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)
- $750
- $6525
- $2332
- $8948
Solutions
Expert Solution
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
orchestra answered 2 years agoRelated Solutions
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