Question
In: Statistics and Probability
Shown below is a portion of the computer output for a regression analysis relating sales (Y...
- Shown below is a portion of the computer output for a regression analysis relating sales (Y in millions of dollars) and advertising expenditure (X in thousands of dollars).
|
Predictor |
Coefficient |
Standard Error |
|
Constant |
4.00 |
0.800 |
|
X |
-0.12 |
0.045 |
Analysis of Variance
|
SOURCE |
DF |
SS |
|
Regression |
1 |
1,400 |
|
Error |
18 |
3,600 |
Please answer the following questions with showing all the steps needed.
a. (8’) What has been the sample size for the above? Please explain how you obtain the answer using the numbers from the question?
b. (32’) Perform a t test and determine whether or not advertising and sales are related. Let a = 0.05.
c. (28’) Compute and interpret the coefficient of determination and correlation coefficient
d. (8’) Use the estimated regression equation and predict sales for an advertising expenditure of $4,000. Give your answer in dollars.
f. (24’) At the significant level of 0.1, please derive both P-value and critical value in an F test to determine whether or not advertising and sales are related. Explain your conclusion.
Solutions
orchestra answered 1 year agoRelated Solutions
Shown below is a portion of a computer output for a regression analysis relating Y (demand)...
Shown below is a portion of a computer output for a regression
analysis relating Y (demand) and X (unit price). ANOVA df SS
Regression 1 Error 3132.661 Total 47 8181.479 Coefficients Standard
Error Intercept 80.390 3.102 X -2.137 0.248 (a) Compute the
coefficient of determination and fully interpret its meaning. Be
very specific. (b) Find the standard error for b1 (Sb1). (c)
Perform a t test and determine whether or not demand and unit price
are related. Let =...
Shown below is a portion of an Excel output for regression analysis relating Y (dependent variable)...
Shown below is a portion of an Excel output for regression
analysis relating Y (dependent variable) and X (independent
variable).
ANOVA
df
SS
Regression
1
39947.80
Residual (Error)
10
8280.81
Total
11
48228.61
Coefficients
Standard Error
t Stat
P-value
Intercept
69.190
26.934
2.569
0.02795
X
2.441
0.351
6.946
0.00004
1. What is the estimated regression equation
that relates Y to X? (2 Points)
2. Is the regression relationship significant?
Use the p-value approach and alpha = 0.05 to answer this question.
(2...
A computer manufacturer has developed a regression model relating his sales (Y in $10,000s) with three...
A computer manufacturer has developed a regression model
relating his sales (Y in $10,000s) with three independent
variables. The three independent variables are price per unit
(Price in $100s), advertising (ADV in $1,000s) and the number of
product lines (Lines). Part of the regression results is shown
below.
Coefficient
Standard Error
Intercept
1.0211
22.8752
Price
-0.1524
0.1411
ADV
0.8849
0.2886
Lines
-0.1463
1.5340
Analysis of Variance
Source of
Variation
Degrees
of Freedom
Sum of
Squares
Regression
2708.61
Error (Residuals)
Required:...
A computer manufacturer has developed a regression model relating his sales (Y in $10,000s) with three...
A computer manufacturer has developed a regression model
relating his sales (Y in $10,000s) with three independent
variables. The three independent variables are price per unit
(Price in $100s), advertising (ADV in $1,000s) and the number of
product lines (Lines). Part of the regression results is shown
below.
Coefficient
Standard Error
Intercept
1.0211
22.8752
Price
-0.1524
0.1411
ADV
0.8849
0.2886
Lines
-0.1463
1.5340
Analysis of Variance
Source of
Variation
Degrees
of Freedom
Sum of
Squares
Regression
2708.61
Error (Residuals)
Required:...
Below you are given a partial computer output from a multiple regression analysis based on a...
Below you are given a partial computer output from a multiple
regression analysis based on a sample of 16 observations.
Coefficients Standard Error Constant 12.924 4.425 x1 -3.682 2.630
x2 45.216 12.560 Analysis of Variance Source of Variation Degrees
of Freedom Sum of Squares Mean Square F Regression 4853 2426.5
Error 485.3 Carry out the test of significance for the variable
x1 at the 1% level. The null hypothesis should be options: be
tested for β₃ instead. be rejected....
Shown below is a partial Excel output from a regression analysis. ANOVA df SS MS F...
Shown below is a partial Excel output from a regression
analysis.
ANOVA
df
SS
MS
F
Regression
60
Residual
Total
19
140
Coefficients
Standard Error
Intercept
10.00
2.00
x1
-2.00
1.50
x2
6.00
2.00
x3
-4.00
1.00
a.
Use the above results and write the regression equation. [4
Marks]
b.
Compute the coefficient of determination and fully interpret its
meaning. [4 Marks]
c.
Is the regression model significant? Perform the test at let α =
0.05. [4 Marks]
d.
At...
Shown below is a partial Excel output from a regression analysis. ANOVA df SS MS F...
Shown below is a partial Excel output from a regression
analysis.
ANOVA
df
SS
MS
F
Regression
60
Residual
Total
19
140
Coefficients
Standard Error
Intercept
10.00
2.00
x1
-2.00
1.50
x2
6.00
2.00
x3
-4.00
1.00
a.
Use the above results and write the regression equation. [4
Marks]
b.
Compute the coefficient of determination and fully interpret its
meaning. [4 Marks]
c.
Is the regression model significant? Perform the test at let α =
0.05. [4 Marks]
d.
At...
A regression analysis relating a company’s sales, their advertising expenditure, price, and time resulted in the...
A regression analysis relating a company’s sales, their
advertising expenditure, price, and time resulted in the
following.
Regression Statistics
Multiple R
0.8800
R Square
0.7744
Adjusted R Square
0.7560
Standard Error
232.29
Observations
25
ANOVA
df
SS
MS
F
Significance F
Regression
3
53184931.86
17728310.62
328.56
0.0000
Residual
21
1133108.30
53957.54
Total
24
54318040.16
Coefficients
Standard Error
t Stat
P-value
Intercept
927.23
1229.86
0.75
0.4593
Advertising (X1)
1.02
3.09
0.33
0.7450
Price (X2)
15.61
5.62
2.78
0.0112
Time (X3)
170.53...
Below you are given a partial computer output based on a sample of 8 observations relating...
Below you are given a partial computer output based on a sample
of 8 observations relating an independent variable ( x)
and a dependent variable ( y).
Coefficient
Standard Error
Intercept
13.251
10.77
x
0.803
0.385
ANOVA
SS
Regression
Error (Residual)
41.674
Total
71.875
a.
Develop the estimated regression equation.
b.
At α = .05, test for the significance of the
slope.
c.
At α = .05, perform an F test.
d.
Determine the coefficient of determination.
The following output was obtained from a regression analysis of the dependent variable Sales volume and...
The following output was obtained from a regression analysis of
the dependent variable Sales volume and an independent variable
“location distance from the downtown
branch.
ANOVA
df
SS
MS
F
Regression
2
552.137
267.069
24.235
Residual
10
110.22
11.02
Total
12
662.357
Coefficients
Standard Error
t Stat
P-value
Intercept
-38.623
3.630
12.569
0.000
Location distance
0.309
0.016
6.552
0.000
Calculate and interpret the correlation coefficient. What does
it tell us? (1.5 marks)
Calculate and interpret the coefficient of determination. (1.5...
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