The commercial division of a real estate firm is conducting a regression analysis of the relationship between x, annual gross rents (in thousands of dollars), and y, selling price (in thousands of dollars) for apartment buildings. Data were collected on several properties recently sold and the following computer output was obtained. Analysis of Variance SOURCE Regression Error Total Predictor Constant X Adj SS DE 1 41587.3 7 8 Coef 20.000 SE Coef 3.2213 7.210 1.3626 Regression Equation Y=20.0 +7.21 X 51984.1 (a) How many apartment buildings were in the sample? (b) Write the estimated regression equation. ŷ= (c) What is the value of Sp? I-Value 6.21 5.29 (d) Use the E statistic to test the significance of the relationshin at a 0.05 level of significance
The commercial division of a real estate firm is conducting a regression analysis of the relationship between x, annual gross rents (in thousands of dollars), and y, selling price (in thousands of dollars) for apartment buildings. Data were collected on several properties recently sold and the following computer output was obtained. Analysis of Variance SOURCE Regression Error Total Predictor Constant X Adj SS DE 1 41587.3 7 8 Coef 20.000 SE Coef 3.2213 7.210 1.3626 Regression Equation Y=20.0 +7.21 X 51984.1 (a) How many apartment buildings were in the sample? (b) Write the estimated regression equation. ŷ= (c) What is the value of Sp? I-Value 6.21 5.29 (d) Use the E statistic to test the significance of the relationshin at a 0.05 level of significance
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section: Chapter Questions
Problem 9SGR
Related questions
Question
![### Statistical Analysis Exercise
**Task:**
1. **Find the value of the test statistic.**
- *(Round your answer to two decimal places.)*
- [Input Box]
2. **Find the p-value.**
- *(Round your answer to three decimal places.)*
- *p-value =* [Input Box]
3. **State your conclusion.**
- [ ] Reject \( H_0 \). We cannot conclude that the relationship between selling price (in thousands of dollars) and annual gross rents (in thousands of dollars) is significant.
- [ ] Do not reject \( H_0 \). We cannot conclude that the relationship between selling price (in thousands of dollars) and annual gross rents (in thousands of dollars) is significant.
- [ ] Reject \( H_0 \). We conclude that the relationship between selling price (in thousands of dollars) and annual gross rents (in thousands of dollars) is significant.
- [ ] Do not reject \( H_0 \). We conclude that the relationship between selling price (in thousands of dollars) and annual gross rents (in thousands of dollars) is significant.
4. **Prediction Task:**
- **Predict the selling price (in thousands of dollars) of an apartment building with gross annual rents of $45,000.**
- $ [Input Box] thousand
This exercise is designed to test your understanding of hypothesis testing and prediction using statistical methods. Be sure to carefully consider each option and use appropriate statistical tables and formulas where necessary.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff7b76bbb-1122-4c75-9c9e-2038b7c47d4e%2F80174438-918d-4793-9631-c0169287ce85%2F2n2753l_processed.png&w=3840&q=75)
Transcribed Image Text:### Statistical Analysis Exercise
**Task:**
1. **Find the value of the test statistic.**
- *(Round your answer to two decimal places.)*
- [Input Box]
2. **Find the p-value.**
- *(Round your answer to three decimal places.)*
- *p-value =* [Input Box]
3. **State your conclusion.**
- [ ] Reject \( H_0 \). We cannot conclude that the relationship between selling price (in thousands of dollars) and annual gross rents (in thousands of dollars) is significant.
- [ ] Do not reject \( H_0 \). We cannot conclude that the relationship between selling price (in thousands of dollars) and annual gross rents (in thousands of dollars) is significant.
- [ ] Reject \( H_0 \). We conclude that the relationship between selling price (in thousands of dollars) and annual gross rents (in thousands of dollars) is significant.
- [ ] Do not reject \( H_0 \). We conclude that the relationship between selling price (in thousands of dollars) and annual gross rents (in thousands of dollars) is significant.
4. **Prediction Task:**
- **Predict the selling price (in thousands of dollars) of an apartment building with gross annual rents of $45,000.**
- $ [Input Box] thousand
This exercise is designed to test your understanding of hypothesis testing and prediction using statistical methods. Be sure to carefully consider each option and use appropriate statistical tables and formulas where necessary.
![The commercial division of a real estate firm is conducting a regression analysis of the relationship between \( x \), annual gross rents (in thousands of dollars), and \( y \), selling price (in thousands of dollars) for apartment buildings. Data were collected on several properties recently sold and the following computer output was obtained.
### Analysis of Variance
- **SOURCE**:
- **DF**: Degrees of Freedom
- **Adj SS**: Adjusted Sum of Squares
- **Regression**:
- DF: 1
- Adj SS: 41587.3
- **Error**:
- DF: 7
- Adj SS: (Not specified)
- **Total**:
- DF: 8
- Adj SS: 51984.1
### Predictor Variables
- **Predictor**: Includes Constant and X (the variable in question)
- **Coeff**: Coefficient
- **SE Coeff**: Standard Error of Coefficient
- **T-Value**: Test statistic
- **Constant**:
- Coeff: 20.000
- SE Coeff: 3.2213
- T-Value: 6.21
- **X**:
- Coeff: 7.210
- SE Coeff: 1.3626
- T-Value: 5.29
### Regression Equation
\[ Y = 20.0 + 7.21X \]
### Questions:
(a) **How many apartment buildings were in the sample?**
(b) **Write the estimated regression equation.**
\[ \hat{Y} = \]
(c) **What is the value of \( s_{b_1} \)?**
(d) **Use the F statistic to test the significance of the relationship at a 0.05 level of significance.**
**State the null and alternative hypotheses.**
- \( H_0: \beta_1 = 0 \)
- \( H_a: \beta_1 \neq 0 \)
- \( H_0: \beta_1 \neq 0 \)
- \( H_a: \beta_1 = 0 \)
- \( H_0: \beta_1 \geq 0 \)
- \( H_a: \beta_1 < 0 \)
- \( H_0:](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff7b76bbb-1122-4c75-9c9e-2038b7c47d4e%2F80174438-918d-4793-9631-c0169287ce85%2Fvmxlzto_processed.png&w=3840&q=75)
Transcribed Image Text:The commercial division of a real estate firm is conducting a regression analysis of the relationship between \( x \), annual gross rents (in thousands of dollars), and \( y \), selling price (in thousands of dollars) for apartment buildings. Data were collected on several properties recently sold and the following computer output was obtained.
### Analysis of Variance
- **SOURCE**:
- **DF**: Degrees of Freedom
- **Adj SS**: Adjusted Sum of Squares
- **Regression**:
- DF: 1
- Adj SS: 41587.3
- **Error**:
- DF: 7
- Adj SS: (Not specified)
- **Total**:
- DF: 8
- Adj SS: 51984.1
### Predictor Variables
- **Predictor**: Includes Constant and X (the variable in question)
- **Coeff**: Coefficient
- **SE Coeff**: Standard Error of Coefficient
- **T-Value**: Test statistic
- **Constant**:
- Coeff: 20.000
- SE Coeff: 3.2213
- T-Value: 6.21
- **X**:
- Coeff: 7.210
- SE Coeff: 1.3626
- T-Value: 5.29
### Regression Equation
\[ Y = 20.0 + 7.21X \]
### Questions:
(a) **How many apartment buildings were in the sample?**
(b) **Write the estimated regression equation.**
\[ \hat{Y} = \]
(c) **What is the value of \( s_{b_1} \)?**
(d) **Use the F statistic to test the significance of the relationship at a 0.05 level of significance.**
**State the null and alternative hypotheses.**
- \( H_0: \beta_1 = 0 \)
- \( H_a: \beta_1 \neq 0 \)
- \( H_0: \beta_1 \neq 0 \)
- \( H_a: \beta_1 = 0 \)
- \( H_0: \beta_1 \geq 0 \)
- \( H_a: \beta_1 < 0 \)
- \( H_0:
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