The following estimated regression equation relating sales to inventory investment and advertising expenditures was given. ý = 24 + 14x, + 6x2 The data used to develop the model came from a survey of 10 stores; for those data, SST = 19,000 and SSR = 15,010. (a) For the estimated regression equation given, compute R2. R2 = (b) Compute R 2. (Round your answer to two decimal places.) R,2 = [ (c) Does the model appear to explain a large amount of variability the data? Explain. (For purposes of this exercise, consider an amount large if it is at least 55%. Round your answer to the nearest integer.) The adjusted coefficient of determination shows that % of the variability has been explained by the two independent variables; thus, we conclude that the model --Select-- v explain a large amount of variability.

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**Regression Analysis Exercise**

The following estimated regression equation relating sales to inventory investment and advertising expenditures was given:

\[ y = 24 + 14x_1 + 6x_2 \]

The data used to develop the model came from a survey of 10 stores; for those data, SST = 19,000 and SSR = 15,010.

### Tasks:

**(a) Compute \( R^2 \):**
- For the estimated regression equation given, compute the coefficient of determination \( R^2 \).

\[ R^2 = \_\_\_\_\_\_ \]

**(b) Compute \( R^2_a \):**
- Compute the adjusted \( R^2 \). (Round your answer to two decimal places.)

\[ R^2_a = \_\_\_\_\_\_ \]

**(c) Evaluate Model Variability:**
- Does the model appear to explain a large amount of variability in the data? Explain. (For purposes of this exercise, consider an amount large if it is at least 55%. Round your answer to the nearest integer.)

The adjusted coefficient of determination shows that \_\_\_\_\_\_ % of the variability has been explained by the two independent variables; thus, we conclude that the model \_\_\_\_\_\_ (use "Select" dropdown to indicate if it explains a large amount of variability or not).
Transcribed Image Text:**Regression Analysis Exercise** The following estimated regression equation relating sales to inventory investment and advertising expenditures was given: \[ y = 24 + 14x_1 + 6x_2 \] The data used to develop the model came from a survey of 10 stores; for those data, SST = 19,000 and SSR = 15,010. ### Tasks: **(a) Compute \( R^2 \):** - For the estimated regression equation given, compute the coefficient of determination \( R^2 \). \[ R^2 = \_\_\_\_\_\_ \] **(b) Compute \( R^2_a \):** - Compute the adjusted \( R^2 \). (Round your answer to two decimal places.) \[ R^2_a = \_\_\_\_\_\_ \] **(c) Evaluate Model Variability:** - Does the model appear to explain a large amount of variability in the data? Explain. (For purposes of this exercise, consider an amount large if it is at least 55%. Round your answer to the nearest integer.) The adjusted coefficient of determination shows that \_\_\_\_\_\_ % of the variability has been explained by the two independent variables; thus, we conclude that the model \_\_\_\_\_\_ (use "Select" dropdown to indicate if it explains a large amount of variability or not).
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