Use computer software packages, such as Minitab or Excel, to solve this problem. Consider the following data for two variables, a and y. 25 27 29 33 38 43 10 19 31 33 38 34 a. Develop an estimated regression equation for the data of the form ŷ = bo + b1æ (to 2 decimals, if necessary). Enter negative value as negative number. b. Using the results from part (a), test for a significiant relationship between 2 and y;use a = 0.05. What is the value of the coefficient of determination (to 3 decimals)? (to 3 decimals) What is the value of the F test statistic (to 2 decimals)?
Use computer software packages, such as Minitab or Excel, to solve this problem. Consider the following data for two variables, a and y. 25 27 29 33 38 43 10 19 31 33 38 34 a. Develop an estimated regression equation for the data of the form ŷ = bo + b1æ (to 2 decimals, if necessary). Enter negative value as negative number. b. Using the results from part (a), test for a significiant relationship between 2 and y;use a = 0.05. What is the value of the coefficient of determination (to 3 decimals)? (to 3 decimals) What is the value of the F test statistic (to 2 decimals)?
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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Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
Question
![Use computer software packages, such as Minitab or Excel, to solve this problem.
Consider the following data for two variables, \( x \) and \( y \):
\[
\begin{array}{|c|c|c|c|c|c|c|}
\hline
x & 25 & 27 & 29 & 33 & 38 & 43 \\
\hline
y & 10 & 19 & 31 & 33 & 38 & 34 \\
\hline
\end{array}
\]
**a.** Develop an estimated regression equation for the data of the form \( \hat{y} = b_0 + b_1 x \) (to 2 decimals, if necessary). Enter negative value as negative number.
\[
\hat{y} =\ \_\_\_\ +\ \_\_\_\ x
\]
**b.** Using the results from part (a), test for a significant relationship between \( x \) and \( y \); use \( \alpha = 0.05 \).
- What is the value of the coefficient of determination (to 3 decimals)?
\[
\_\_\_\
\]
- What is the value of the \( F \) test statistic (to 2 decimals)?
\[
\_\_\_\
\]
- What is the \( p \)-value?
\[
\_\_\_\
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F56b29ac1-2bc2-4707-9f70-7bacc854483d%2F5e405982-7b70-4c6d-8d39-d17d7d0f8d17%2F3tgmnrv_processed.gif&w=3840&q=75)
Transcribed Image Text:Use computer software packages, such as Minitab or Excel, to solve this problem.
Consider the following data for two variables, \( x \) and \( y \):
\[
\begin{array}{|c|c|c|c|c|c|c|}
\hline
x & 25 & 27 & 29 & 33 & 38 & 43 \\
\hline
y & 10 & 19 & 31 & 33 & 38 & 34 \\
\hline
\end{array}
\]
**a.** Develop an estimated regression equation for the data of the form \( \hat{y} = b_0 + b_1 x \) (to 2 decimals, if necessary). Enter negative value as negative number.
\[
\hat{y} =\ \_\_\_\ +\ \_\_\_\ x
\]
**b.** Using the results from part (a), test for a significant relationship between \( x \) and \( y \); use \( \alpha = 0.05 \).
- What is the value of the coefficient of determination (to 3 decimals)?
\[
\_\_\_\
\]
- What is the value of the \( F \) test statistic (to 2 decimals)?
\[
\_\_\_\
\]
- What is the \( p \)-value?
\[
\_\_\_\
\]
![### Instructions for Regression Analysis
#### Part d:
- **Objective:** Develop an estimated regression equation for the data of the form \( \hat{y} = b_0 + b_1 x + b_2 x^2 \).
- **Output Format:** Provide estimates to 3 decimal places. Enter any negative values as negative numbers.
\[ \hat{y} = (\text{Enter } b_0) + (\text{Enter } b_1) x + (\text{Enter } b_2)x^2 \]
#### Part e:
- **Task:** Refer to the regression equation developed in Part d.
- **Objective:** Determine if the relationship between \( x, x^2, \) and \( y \) is significant using \( \alpha = 0.05 \).
1. **Coefficient of Determination:**
- Calculate and enter to 3 decimal places.
- **Input:** [Text box provided]
2. **F Test Statistic Value:**
- Calculate and enter to 2 decimal places.
- **Input:** [Text box provided]
3. **P-Value:**
- **Input:** [Dropdown menu for selection]
4. **Conclusion Using \( \alpha = 0.05\):**
- **Input:** [Dropdown menu for selection]
#### Part f:
- **Prediction Task:** Predict the value of \( y \) when \( x = 25 \).
- **Output Format:** Give prediction to 2 decimal places.
- **Input:** [Text box provided]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F56b29ac1-2bc2-4707-9f70-7bacc854483d%2F5e405982-7b70-4c6d-8d39-d17d7d0f8d17%2F6h8znh_processed.gif&w=3840&q=75)
Transcribed Image Text:### Instructions for Regression Analysis
#### Part d:
- **Objective:** Develop an estimated regression equation for the data of the form \( \hat{y} = b_0 + b_1 x + b_2 x^2 \).
- **Output Format:** Provide estimates to 3 decimal places. Enter any negative values as negative numbers.
\[ \hat{y} = (\text{Enter } b_0) + (\text{Enter } b_1) x + (\text{Enter } b_2)x^2 \]
#### Part e:
- **Task:** Refer to the regression equation developed in Part d.
- **Objective:** Determine if the relationship between \( x, x^2, \) and \( y \) is significant using \( \alpha = 0.05 \).
1. **Coefficient of Determination:**
- Calculate and enter to 3 decimal places.
- **Input:** [Text box provided]
2. **F Test Statistic Value:**
- Calculate and enter to 2 decimal places.
- **Input:** [Text box provided]
3. **P-Value:**
- **Input:** [Dropdown menu for selection]
4. **Conclusion Using \( \alpha = 0.05\):**
- **Input:** [Dropdown menu for selection]
#### Part f:
- **Prediction Task:** Predict the value of \( y \) when \( x = 25 \).
- **Output Format:** Give prediction to 2 decimal places.
- **Input:** [Text box provided]
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