X₂ of cases) of the cold remedy sing (x $1,000) for the cold remedy similar products (x $10,000) cerning the regression model: ).640, se = 1.63, F-statistic = 31.402, and Durbin-Watson (d) statistic = 0.499. s (if any) appears to be statistically significant (at the 0.05 level) in explaining sales of the col mat apply. tion in sales is explained by the regression equation? reject the null hypothesis that neither of the independent variables explains a sig income. (Hint: Fo.05,2,33-2-1=3.316.)
X₂ of cases) of the cold remedy sing (x $1,000) for the cold remedy similar products (x $10,000) cerning the regression model: ).640, se = 1.63, F-statistic = 31.402, and Durbin-Watson (d) statistic = 0.499. s (if any) appears to be statistically significant (at the 0.05 level) in explaining sales of the col mat apply. tion in sales is explained by the regression equation? reject the null hypothesis that neither of the independent variables explains a sig income. (Hint: Fo.05,2,33-2-1=3.316.)
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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![### Analysis of Sales Data for Cascade Pharmaceuticals Company
Cascade Pharmaceuticals Company developed a regression model to examine the sales determinants of one of its nonprescription cold remedies. The analysis used time-series data over the past 33 quarters.
#### The Regression Equation:
\[
Y = -1.04 + 0.24X_1 - 0.27X_2
\]
Where:
- \( Y \) denotes quarterly sales (in thousands of cases) of the cold remedy.
- \( X_1 \) is Cascade’s quarterly advertising expenditure (in $1,000s) for the cold remedy.
- \( X_2 \) represents competitors’ advertising expenditure for similar products (in $10,000s).
#### Summary of Regression Model:
- \( s_{b1} = 0.052 \)
- \( s_{b2} = 0.070 \)
- \( R^2 = 0.640 \)
- \( s_e = 1.63 \)
- \( F\text{-statistic} = 31.402 \)
- \( \text{Durbin-Watson (d) statistic} = 0.499 \)
#### Analysis
1. **Significance of Independent Variables:**
Question: Which of the independent variables (if any) appears to be statistically significant (at the 0.05 level) in explaining sales of the cold remedy?
Hint: \( t_{0.05/2, 33-3} = 2.042 \). Check all that apply.
- [ ] \( X_1 \)
- [ ] \( X_2 \)
2. **Proportion of Total Variation in Sales:**
Question: What proportion of the total variation in sales is explained by the regression equation?
- [ ] 0.122
- [ ] 0.070
- [ ] 0.640
- [ ] 0.052
3. **Hypothesis Testing:**
The given F-value shows that you _______ reject the null hypothesis that neither of the independent variables explains a significant (at the 0.05 level) proportion of the variation in sales.
Hint: \( F_{0.05,2,33-2} = 3.316 \).
To utilize this regression analysis, it is essential to assess the values of \( b_1 \) and \( b_](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F94a8cceb-0882-4bfc-b07b-9c756050dcc4%2Fe0e9d4ad-4660-4748-87bf-3e7fdc69e6c5%2Fsl2mhpc_processed.png&w=3840&q=75)
Transcribed Image Text:### Analysis of Sales Data for Cascade Pharmaceuticals Company
Cascade Pharmaceuticals Company developed a regression model to examine the sales determinants of one of its nonprescription cold remedies. The analysis used time-series data over the past 33 quarters.
#### The Regression Equation:
\[
Y = -1.04 + 0.24X_1 - 0.27X_2
\]
Where:
- \( Y \) denotes quarterly sales (in thousands of cases) of the cold remedy.
- \( X_1 \) is Cascade’s quarterly advertising expenditure (in $1,000s) for the cold remedy.
- \( X_2 \) represents competitors’ advertising expenditure for similar products (in $10,000s).
#### Summary of Regression Model:
- \( s_{b1} = 0.052 \)
- \( s_{b2} = 0.070 \)
- \( R^2 = 0.640 \)
- \( s_e = 1.63 \)
- \( F\text{-statistic} = 31.402 \)
- \( \text{Durbin-Watson (d) statistic} = 0.499 \)
#### Analysis
1. **Significance of Independent Variables:**
Question: Which of the independent variables (if any) appears to be statistically significant (at the 0.05 level) in explaining sales of the cold remedy?
Hint: \( t_{0.05/2, 33-3} = 2.042 \). Check all that apply.
- [ ] \( X_1 \)
- [ ] \( X_2 \)
2. **Proportion of Total Variation in Sales:**
Question: What proportion of the total variation in sales is explained by the regression equation?
- [ ] 0.122
- [ ] 0.070
- [ ] 0.640
- [ ] 0.052
3. **Hypothesis Testing:**
The given F-value shows that you _______ reject the null hypothesis that neither of the independent variables explains a significant (at the 0.05 level) proportion of the variation in sales.
Hint: \( F_{0.05,2,33-2} = 3.316 \).
To utilize this regression analysis, it is essential to assess the values of \( b_1 \) and \( b_
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