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Variable Intercept X Z XZ Y Sum 18.00000 263.80000 9.00000 126.80000 2597.50000 Source Model Error Corrected Total Variable Intercept X Z XZ Mean 1.00000 14.65556 0.50000 7.04444 144.30556 DF 1 1 1 1 DF 3 age Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the ellook and o ned that any suppressed content does not materially affect the overall leaming experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights r 14 17 Root MSE Dependent Mean Coeff Var Uncorrected SS 18.00000 4002.94000 9.00000 1851.44000 376639 ANALYSIS OF VARIANCE Sum of Squares 1755.87993 49.16951 1805.04944 Parameter Estimate 96.83045 3.48486 7.17269 -1.01978 PARAMETER ESTIMATES Standard Error Variance 1.87406 R-Square 144.30556 Adj R-Sq 1.29868 3.56516 0.23058 4.88170 0.32746 0 8.04732 0.26471 56.36497 106.17938 Mean Square 585.29331 3.51211 t Value F Value 166.65 Pr>t Standard Deviation 0.9728 0.9669 27.16 <.0001 15.11 <.0001 1.47 0.1639 -3.11 0.0076 2.83678 0.51450 7.50766 10.30434 Pr > F <.0001 Type I SS 374834 (continued) 1461.75022 260.06703 34.06268 Problems

Variable Intercept X Z XZ Y Sum 18.00000 263.80000 9.00000 126.80000 2597.50000 Source Model Error Corrected Total Variable Intercept X Z XZ Mean 1.00000 14.65556 0.50000 7.04444 144.30556 DF 1 1 1 1 DF 3 age Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the ellook and o ned that any suppressed content does not materially affect the overall leaming experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights r 14 17 Root MSE Dependent Mean Coeff Var Uncorrected SS 18.00000 4002.94000 9.00000 1851.44000 376639 ANALYSIS OF VARIANCE Sum of Squares 1755.87993 49.16951 1805.04944 Parameter Estimate 96.83045 3.48486 7.17269 -1.01978 PARAMETER ESTIMATES Standard Error Variance 1.87406 R-Square 144.30556 Adj R-Sq 1.29868 3.56516 0.23058 4.88170 0.32746 0 8.04732 0.26471 56.36497 106.17938 Mean Square 585.29331 3.51211 t Value F Value 166.65 Pr>t Standard Deviation 0.9728 0.9669 27.16 <.0001 15.11 <.0001 1.47 0.1639 -3.11 0.0076 2.83678 0.51450 7.50766 10.30434 Pr > F <.0001 Type I SS 374834 (continued) 1461.75022 260.06703 34.06268 Problems

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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**Market Research on Seasonal Advertising and Sales Revenue** Market research was conducted for a national retail company to explore the relationship between sales and advertising during the warm spring and summer seasons as well as the cool fall and winter seasons. The data revealed was collected over several years and is presented in the table below. **Data Table:** - **Warm Season (Warm = 0)** - Advertising Expenditure ($ millions): 17.0, 12.5, 20.5, 16.0, 15.0, 14.5, 17.5, 12.5, 11.5 - Sales Revenue ($ millions): 156.1, 142.6, 166.8, 155.4, 150.5, 147.5, 156.9, 138.8, 134.3 - **Cool Season (Warm = 0, Cool = 1)** - Advertising Expenditure ($ millions): 10.0, 13.8, 15.0, 19.5, 17.0, 12.5, 14.5, 12.5, 12.0 - Sales Revenue ($ millions): 131.0, 136.8, 141.5, 151.8, 148.3, 133.3, 138.0, 135.9, 132.0 **Exercises:** a. **Regression Modeling:** Identify a single regression model using data for both warm and cool seasons. This model should define straight-line models relating sales revenue (Y) to advertising expenditure (X) for each season. b. **Fitting Straight Lines:** Using the provided computer output, determine and plot the fitted straight lines for each season. c. **Testing Coincidence of Lines:** Test whether the straight lines for cool and warm seasons coincide. d. **Parallelism Test:** Test the hypothesis \( H_0: \) "The lines are parallel" versus \( H_4: \) "The lines are not parallel." e. **Analysis of Results:** In light of your answers to parts (c) and (d), comment on the differences and similarities in the sales-advertising expenditure relationship between cooler and warmer seasons. --- This structured analysis will help understand seasonal variations in retail sales and the effectiveness of advertising strategies.
Transcribed Image Text:**Market Research on Seasonal Advertising and Sales Revenue** Market research was conducted for a national retail company to explore the relationship between sales and advertising during the warm spring and summer seasons as well as the cool fall and winter seasons. The data revealed was collected over several years and is presented in the table below. **Data Table:** - **Warm Season (Warm = 0)** - Advertising Expenditure ($ millions): 17.0, 12.5, 20.5, 16.0, 15.0, 14.5, 17.5, 12.5, 11.5 - Sales Revenue ($ millions): 156.1, 142.6, 166.8, 155.4, 150.5, 147.5, 156.9, 138.8, 134.3 - **Cool Season (Warm = 0, Cool = 1)** - Advertising Expenditure ($ millions): 10.0, 13.8, 15.0, 19.5, 17.0, 12.5, 14.5, 12.5, 12.0 - Sales Revenue ($ millions): 131.0, 136.8, 141.5, 151.8, 148.3, 133.3, 138.0, 135.9, 132.0 **Exercises:** a. **Regression Modeling:** Identify a single regression model using data for both warm and cool seasons. This model should define straight-line models relating sales revenue (Y) to advertising expenditure (X) for each season. b. **Fitting Straight Lines:** Using the provided computer output, determine and plot the fitted straight lines for each season. c. **Testing Coincidence of Lines:** Test whether the straight lines for cool and warm seasons coincide. d. **Parallelism Test:** Test the hypothesis \( H_0: \) "The lines are parallel" versus \( H_4: \) "The lines are not parallel." e. **Analysis of Results:** In light of your answers to parts (c) and (d), comment on the differences and similarities in the sales-advertising expenditure relationship between cooler and warmer seasons. --- This structured analysis will help understand seasonal variations in retail sales and the effectiveness of advertising strategies.
### Data Analysis and Interpretation #### Summary Statistics Table This table provides summary statistics for various variables, including: - **Variable Names:** Intercept, X, Z, XZ, and Y. - **Sum:** Total of all observations for each variable. - **Mean:** Average of observations for each variable. - **Uncorrected SS (Sum of Squares):** Measure of the total variability in the observations. - **Variance:** Measure of the spread of the data around the mean. - **Standard Deviation:** Square root of the variance, representing dispersion of the dataset. Values for each variable: - **Intercept:** - Sum: 18.00000 - Mean: 1.00000 - Uncorrected SS: 18.00000 - Variance: 0 - Standard Deviation: 0 - **X:** - Sum: 263.80000 - Mean: 14.65556 - Uncorrected SS: 4020.94000 - Variance: 8.04732 - Standard Deviation: 2.83678 - **Z:** - Sum: 9.00000 - Mean: 0.50000 - Uncorrected SS: 9.00000 - Variance: 0.26471 - Standard Deviation: 0.51450 - **XZ:** - Sum: 126.80000 - Mean: 7.04444 - Uncorrected SS: 1851.44000 - Variance: 56.36497 - Standard Deviation: 7.50766 - **Y:** - Sum: 2597.50000 - Mean: 144.30556 - Uncorrected SS: 376639 - Variance: 106.17938 - Standard Deviation: 10.30434 --- #### Analysis of Variance (ANOVA) Table The ANOVA table summarizes the analysis of variance for the dataset: - **Source:** - **Model** - DF (Degrees of Freedom): 3 - Sum of Squares: 1755.87993 - Mean Square: 585.29331 - F Value: 166.
Transcribed Image Text:### Data Analysis and Interpretation #### Summary Statistics Table This table provides summary statistics for various variables, including: - **Variable Names:** Intercept, X, Z, XZ, and Y. - **Sum:** Total of all observations for each variable. - **Mean:** Average of observations for each variable. - **Uncorrected SS (Sum of Squares):** Measure of the total variability in the observations. - **Variance:** Measure of the spread of the data around the mean. - **Standard Deviation:** Square root of the variance, representing dispersion of the dataset. Values for each variable: - **Intercept:** - Sum: 18.00000 - Mean: 1.00000 - Uncorrected SS: 18.00000 - Variance: 0 - Standard Deviation: 0 - **X:** - Sum: 263.80000 - Mean: 14.65556 - Uncorrected SS: 4020.94000 - Variance: 8.04732 - Standard Deviation: 2.83678 - **Z:** - Sum: 9.00000 - Mean: 0.50000 - Uncorrected SS: 9.00000 - Variance: 0.26471 - Standard Deviation: 0.51450 - **XZ:** - Sum: 126.80000 - Mean: 7.04444 - Uncorrected SS: 1851.44000 - Variance: 56.36497 - Standard Deviation: 7.50766 - **Y:** - Sum: 2597.50000 - Mean: 144.30556 - Uncorrected SS: 376639 - Variance: 106.17938 - Standard Deviation: 10.30434 --- #### Analysis of Variance (ANOVA) Table The ANOVA table summarizes the analysis of variance for the dataset: - **Source:** - **Model** - DF (Degrees of Freedom): 3 - Sum of Squares: 1755.87993 - Mean Square: 585.29331 - F Value: 166.
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