y = demand for the large bottle of Fresh in the sales period(Demand)x1 = the price of product 1x2 = the price of product 2x3 = the advertising expenditure for Freshx4 = the price difference in the sales periodAdver = types of advertising campaignsCampaign A consists entirely of television commercials, campaign B consists of a balancedmixture of television and radio commercials, and campaign C consists of a balanced mixture oftelevision, radio, newspaper, an dmagazine ads. To ultimately increase the demand for Fresh,Enterprise Industries’ marketing department is comparing the effectiveness of three differentadvertising campaigns. To compare the effectiveness of advertising campaigns A, B, and C, wedefine two dummy variables. Specifically, DB is 1 if campaign B is used and 0 otherwise, DC is1 if campaign C is used and 0 otherwise. Our proposed model is y = β0 + β1x4 + β2x3 + β3x 2 3 + β4x4x3 + β5DB + β6DC The image displays a spreadsheet with data organized in columns labeled A through I and rows numbered from 1 to 21.### Columns:- **Column A to Column E**: Contain numerical values that seem to represent different variables or measurements.- **Column F**: Contains categorical data labeled with the letters B, C, or A.- **Column G, H, and I**: Contain binary data with values of 0 or 1.### Rows:- **Rows 1 to 20**: Each row represents a different set of measurements for the variables in columns A to E, a category in column F, and binary indicators in columns G to I.### Observations:- Some rows have small negative values in column D (e.g., -0.15 in row 1).- Column F mixes categorical labels across the dataset.- Columns G, H, and I likely represent boolean conditions or flags.This data could be used to analyze relationships between numerical and categorical variables, or for classification tasks using the binary columns. (a) Estimate $ \beta_i $ for each $ i = 0, 1, 2, 3, 4 $.(b) Set $ \alpha = 0.05 $ and test \[H_0: \beta_i = 0, \quad H_a: \beta_i \neq 0\]for each $ i = 1, 2, 3, 4 $. What do you conclude? Interpret your result based on your hypothesis test on each $ \beta_i $. (Stating that we reject (do not reject) $ H_0 $ or significant (not significant) is not enough. Need to explain the relationship between factors and the consequences.)

Answered: y = demand for the large bottle of…

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

1st Edition

ISBN:9781680331141

Author:HOUGHTON MIFFLIN HARCOURT

Publisher:HOUGHTON MIFFLIN HARCOURT

Chapter4: Writing Linear Equations

Section: Chapter Questions

Problem 12CR

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Question

y = demand for the large bottle of Fresh in the sales period(Demand)
x1 = the price of product 1
x2 = the price of product 2
x3 = the advertising expenditure for Fresh
x4 = the price difference in the sales period
Adver = types of advertising campaigns
Campaign A consists entirely of television commercials, campaign B consists of a balanced
mixture of television and radio commercials, and campaign C consists of a balanced mixture of
television, radio, newspaper, an dmagazine ads. To ultimately increase the demand for Fresh,
Enterprise Industries’ marketing department is comparing the effectiveness of three different
advertising campaigns. To compare the effectiveness of advertising campaigns A, B, and C, we
define two dummy variables. Specifically, DB is 1 if campaign B is used and 0 otherwise, DC is
1 if campaign C is used and 0 otherwise. Our proposed model is

y = β0 + β1x4 + β2x3 + β3x 2 3 + β4x4x3 + β5DB + β6DC

The image displays a spreadsheet with data organized in columns labeled A through I and rows numbered from 1 to 21.

### Columns:
- **Column A to Column E**: Contain numerical values that seem to represent different variables or measurements.
- **Column F**: Contains categorical data labeled with the letters B, C, or A.
- **Column G, H, and I**: Contain binary data with values of 0 or 1.

### Rows:
- **Rows 1 to 20**: Each row represents a different set of measurements for the variables in columns A to E, a category in column F, and binary indicators in columns G to I.

### Observations:
- Some rows have small negative values in column D (e.g., -0.15 in row 1).
- Column F mixes categorical labels across the dataset.
- Columns G, H, and I likely represent boolean conditions or flags.

This data could be used to analyze relationships between numerical and categorical variables, or for classification tasks using the binary columns.

(a) Estimate $ \beta_i $ for each $ i = 0, 1, 2, 3, 4 $.

(b) Set $ \alpha = 0.05 $ and test

\[
H_0: \beta_i = 0, \quad H_a: \beta_i \neq 0
\]

for each $ i = 1, 2, 3, 4 $. What do you conclude? Interpret your result based on your hypothesis test on each $ \beta_i $. (Stating that we reject (do not reject) $ H_0 $ or significant (not significant) is not enough. Need to explain the relationship between factors and the consequences.)

Expert Solution

Step 1: Write the given information

Given the data as

$y$	$x subscript 1$	$x subscript 2$	$x subscript 3$	$x subscript 4$	Adver	DA	DB	DC
3.80	3.65	5.25	-0.15	7.10	B	0	1	0
3.85	4.00	6.00	0.15	8.00	C	0	0	1
3.90	4.10	6.50	0.20	7.89	A	1	0	0
3.90	4.00	6.25	0.10	8.15	C	0	0	1
3.70	4.10	7.00	0.40	9.10	C	0	0	1
3.75	4.20	6.90	0.45	8.86	A	1	0	0
3.75	4.10	6.80	0.35	8.90	B	0	1	0
3.80	4.10	6.80	0.30	8.87	B	0	1	0
3.70	4.20	7.10	0.50	9.26	B	0	1	0
3.80	4.30	7.00	0.50	9.00	A	1	0	0
3.70	4.10	6.80	0.40	8.75	B	0	1	0
3.80	3.75	6.50	-0.05	7.95	B	0	1	0
3.80	3.75	6.25	-0.05	7.65	C	0	0	1
3.75	3.65	6.00	-0.10	7.27	A	1	0	0
3.70	3.90	6.50	0.20	8.00	A	1	0	0
3.55	3.65	7.00	0.10	8.50	A	1	0	0
3.60	4.10	6.80	0.50	8.75	A	1	0	0
3.65	4.25	6.80	0.60	9.21	B	0	1	0
3.70	3.65	6.50	-0.05	8.27	C	0	0	1
3.75	3.75	5.75	0.00	7.67	B	0	1	0
3.80	3.85	5.80	0.05	7.93	C	0	0	1
3.70	4.25	6.80	0.55	9.26	C	0	0	1

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