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A company has recorded data on the weekly sales for its product (y), the unit price of the competitor's product (x), and advertising expenditures (x2). The data resulting from a random sample of 7 weeks follows. Week Price Advertising Sales

A company has recorded data on the weekly sales for its product (y), the unit price of the competitor's product (x), and advertising expenditures (x2). The data resulting from a random sample of 7 weeks follows. Week Price Advertising Sales

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Data Analysis on Weekly Sales** A company has recorded data on weekly sales for its product (denoted as \( y \)), the unit price of a competitor's product (\( x_1 \)), and advertising expenditures (\( x_2 \)). The data from a random sample over 7 weeks is as follows: | Week | Price (\( x_1 \)) | Advertising (\( x_2 \)) | Sales (\( y \)) | |------|--------------------|--------------------------|-----------------| | 1 | 0.33 | 5 | 20 | | 2 | 0.25 | 2 | 14 | | 3 | 0.44 | 7 | 22 | | 4 | 0.40 | 9 | 21 | | 5 | 0.35 | 4 | 16 | | 6 | 0.39 | 8 | 19 | | 7 | 0.29 | 9 | 15 | **Tasks to Complete:** a) **Develop an estimated regression equation:** Create a model to predict Sales (\( y \)) based on the Price of the competitor’s product (\( x_1 \)) and Advertising expenditures (\( x_2 \)). b) **Model Significance:** Determine if the regression model is significant overall, using a significance level of \( \alpha = 0.10 \). c) **Price Significance:** Assess whether Price is significantly related to Sales at \( \alpha = 0.10 \). d) **Advertising Significance:** Evaluate if Advertising has a significant effect on Sales with \( \alpha = 0.10 \). This study aims to explore the impact of competitor pricing and advertising efforts on the company’s sales performance over the observed weeks.
Transcribed Image Text:**Data Analysis on Weekly Sales** A company has recorded data on weekly sales for its product (denoted as \( y \)), the unit price of a competitor's product (\( x_1 \)), and advertising expenditures (\( x_2 \)). The data from a random sample over 7 weeks is as follows: | Week | Price (\( x_1 \)) | Advertising (\( x_2 \)) | Sales (\( y \)) | |------|--------------------|--------------------------|-----------------| | 1 | 0.33 | 5 | 20 | | 2 | 0.25 | 2 | 14 | | 3 | 0.44 | 7 | 22 | | 4 | 0.40 | 9 | 21 | | 5 | 0.35 | 4 | 16 | | 6 | 0.39 | 8 | 19 | | 7 | 0.29 | 9 | 15 | **Tasks to Complete:** a) **Develop an estimated regression equation:** Create a model to predict Sales (\( y \)) based on the Price of the competitor’s product (\( x_1 \)) and Advertising expenditures (\( x_2 \)). b) **Model Significance:** Determine if the regression model is significant overall, using a significance level of \( \alpha = 0.10 \). c) **Price Significance:** Assess whether Price is significantly related to Sales at \( \alpha = 0.10 \). d) **Advertising Significance:** Evaluate if Advertising has a significant effect on Sales with \( \alpha = 0.10 \). This study aims to explore the impact of competitor pricing and advertising efforts on the company’s sales performance over the observed weeks.
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