# Multiple Regression Analysis in SPSS

### Description

Multiple Regression Analysis in SPSS

The purpose of this assignment is to apply multiple regression concepts, interpret multiple regression analysis models, and justify business predictions based upon the analysis.

For this assignment, you will use the “Strength” dataset. You will use SPSS to analyze the dataset and address the questions presented. **Findings should be presented in a Word document ALONG with the SPSS outputs.**

The compressive strength (Y) of concrete is influenced by the mixing proportions and by the time that it is allowed to cure, although the exact relationship between the strength and the components is unknown. The provided data includes the results of n = 1030 concrete strength experiments that include the following:

**Strength**(in MPa): The compressive strength of the concrete.**Age**(in days): The number of days the concrete was allowed to cured.**Coarse_Aggregate**(in kg/m^{3}): The proportion of coarse aggregate in the mix.**Fine_Aggregate**(in kg/m^{3}): The proportion of fine aggregate in the mix.**Cement**(in kg/m^{3}): The proportion of cement in the mix.**Slag**(in kg/m^{3}): The proportion of furnace slag in the mix.**Superplasticizer**(in kg/m^{3}): The proportion of plasticizer in the mix.**Water**(in kg/m^{3}): The proportion of water in the mix.**Ash**(in kg/m^{3}): The proportion of fly ash in the mix.

*Part 1:*

Derive various transformations of compressive strength to determine which transformation, if any, results in a variable that most closely mimics a normal distribution. To do this, plot Q-Q plots after each transformation listed below, and decide which one should be used to build a multiple linear model. Explain your answer and provide the SPSS output as an illustration.

- Strength (no transformation)
- Square root of Strength
- Squared Strength
- (Natural) Log of Strength
- Reciprocal of Strength

*Part 2:*

Based on the transformation selected in Part 1, build a multiple linear regression model with all eight predictors.

- Use t-tests to determine if any of the predictors significantly affect the compressive strength of concrete. Explain why each variable should or should not be included in the model. Assume α = 0.05. Show the appropriate model results to explain your answer.
- If any predictors from question 1 are found to be not significant, remove them and re-run the model to create a reduced model (RM). Are all the remaining variables still statistically significant? Show the appropriate model results to explain your answer.
- Based on the RM, should there be concern about multicollinearity among the predictors selected? Show the appropriate model results to explain your answer.
- After fitting the RM, derive the residual plot (standardized residuals vs. standardized predicted values) and normal probability plot. Interpret each plot.
- What is the coefficient of determination, R
^{2}, of the RM? How would you interpret the R^{2}? - Based on the RM, what would be the new estimated compressive strength that is currently 50 MPa, after a 10-day increase in curing time? Assume all other predictors are held constant.
- How would you interpret the intercept (constant) in the RM? Does the interpretation make sense given the data you used to build the RM?

*Part 3:*

Given the following components and aging time below, what is the estimated compressive strength based on the RM?

**Age:**50 days**Coarse_Aggregate:**900 kg/m^{3}**Fine_Aggregate:**600 kg/m^{3}**Cement:**300 kg/m^{3}**Slag:**200 kg/m^{3}**Superplasticizer:**7 kg/m^{3}**Water:**190 kg/m^{3}**Ash:**70 kg/m^{3}

*Part 4:*

What is a 95% confidence interval of the estimate in Part 3? How would you interpret the 95% confidence interval? (**Hint:** Use the SPSS scoring wizard to address this question.)

APA format is not required, but solid academic writing is expected.

This assignment uses a grading rubric. Please review the rubric prior to beginning the assignment to become familiar with the expectations for successful completion. PLEASE MAKE SURE THAT THE ASSIGNMENT INCLUDES THE FLOWING… Q-Q plot SPSS outputs for each transformation and selection of which plot should be used to build a multiple linear model are complete and correct, Answers to multiple regression analysis questions and supporting SPSS output charts are complete and accurate, The estimated compressive strength based on the RM is complete and accurate, The confidence interval and interpretation of the confidence interval are complete and accurate, Writer is clearly in command of standard, written, academic English. Please do these 2 question also… **QUESTION 1**– Suppose you were asked to investigate which predictors explain the number of minutes that 10- to18-year-old students spend on Twitter. To do so, you build a linear regression model with Twitter usage (Y) measured as the number of minutes per week. The four predictors you include in the model are Height, Weight, Grade Level, and Age of each student. You build four

*simple*linear regression models with Y regressed separately on each predictor, and each predictor is statistically significant. Then you build a multiple linear regression model with Y regressed on all four predictors, but only one predictor, Age, is statistically significant, and the others are not. What is likely going on among the four predictors? If you include more than one of these predictors in the model, what are some problems that can result?

*After building a regression model and performing residual diagnostics, you notice that the errors show severe departures from normality and appear to have nonconstant variance. What steps would you take in this case to resolve the errors? If the problems are not corrected after all steps are taken, what does that imply about the modeling approach you are taking? Explain in detail.*

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### Description

Multiple Regression Analysis in SPSS

The purpose of this assignment is to apply multiple regression concepts, interpret multiple regression analysis models, and justify business predictions based upon the analysis.

For this assignment, you will use the “Strength” dataset. You will use SPSS to analyze the dataset and address the questions presented. **Findings should be presented in a Word document ALONG with the SPSS outputs.**

The compressive strength (Y) of concrete is influenced by the mixing proportions and by the time that it is allowed to cure, although the exact relationship between the strength and the components is unknown. The provided data includes the results of n = 1030 concrete strength experiments that include the following:

**Strength**(in MPa): The compressive strength of the concrete.**Age**(in days): The number of days the concrete was allowed to cured.**Coarse_Aggregate**(in kg/m^{3}): The proportion of coarse aggregate in the mix.**Fine_Aggregate**(in kg/m^{3}): The proportion of fine aggregate in the mix.**Cement**(in kg/m^{3}): The proportion of cement in the mix.**Slag**(in kg/m^{3}): The proportion of furnace slag in the mix.**Superplasticizer**(in kg/m^{3}): The proportion of plasticizer in the mix.**Water**(in kg/m^{3}): The proportion of water in the mix.**Ash**(in kg/m^{3}): The proportion of fly ash in the mix.

*Part 1:*

Derive various transformations of compressive strength to determine which transformation, if any, results in a variable that most closely mimics a normal distribution. To do this, plot Q-Q plots after each transformation listed below, and decide which one should be used to build a multiple linear model. Explain your answer and provide the SPSS output as an illustration.

- Strength (no transformation)
- Square root of Strength
- Squared Strength
- (Natural) Log of Strength
- Reciprocal of Strength

*Part 2:*

Based on the transformation selected in Part 1, build a multiple linear regression model with all eight predictors.

- Use t-tests to determine if any of the predictors significantly affect the compressive strength of concrete. Explain why each variable should or should not be included in the model. Assume α = 0.05. Show the appropriate model results to explain your answer.
- If any predictors from question 1 are found to be not significant, remove them and re-run the model to create a reduced model (RM). Are all the remaining variables still statistically significant? Show the appropriate model results to explain your answer.
- Based on the RM, should there be concern about multicollinearity among the predictors selected? Show the appropriate model results to explain your answer.
- After fitting the RM, derive the residual plot (standardized residuals vs. standardized predicted values) and normal probability plot. Interpret each plot.
- What is the coefficient of determination, R
^{2}, of the RM? How would you interpret the R^{2}? - Based on the RM, what would be the new estimated compressive strength that is currently 50 MPa, after a 10-day increase in curing time? Assume all other predictors are held constant.
- How would you interpret the intercept (constant) in the RM? Does the interpretation make sense given the data you used to build the RM?

*Part 3:*

Given the following components and aging time below, what is the estimated compressive strength based on the RM?

**Age:**50 days**Coarse_Aggregate:**900 kg/m^{3}**Fine_Aggregate:**600 kg/m^{3}**Cement:**300 kg/m^{3}**Slag:**200 kg/m^{3}**Superplasticizer:**7 kg/m^{3}**Water:**190 kg/m^{3}**Ash:**70 kg/m^{3}

*Part 4:*

What is a 95% confidence interval of the estimate in Part 3? How would you interpret the 95% confidence interval? (**Hint:** Use the SPSS scoring wizard to address this question.)

APA format is not required, but solid academic writing is expected.

This assignment uses a grading rubric. Please review the rubric prior to beginning the assignment to become familiar with the expectations for successful completion. PLEASE MAKE SURE THAT THE ASSIGNMENT INCLUDES THE FLOWING… Q-Q plot SPSS outputs for each transformation and selection of which plot should be used to build a multiple linear model are complete and correct, Answers to multiple regression analysis questions and supporting SPSS output charts are complete and accurate, The estimated compressive strength based on the RM is complete and accurate, The confidence interval and interpretation of the confidence interval are complete and accurate, Writer is clearly in command of standard, written, academic English. Please do these 2 question also… **QUESTION 1**– Suppose you were asked to investigate which predictors explain the number of minutes that 10- to18-year-old students spend on Twitter. To do so, you build a linear regression model with Twitter usage (Y) measured as the number of minutes per week. The four predictors you include in the model are Height, Weight, Grade Level, and Age of each student. You build four

*simple*linear regression models with Y regressed separately on each predictor, and each predictor is statistically significant. Then you build a multiple linear regression model with Y regressed on all four predictors, but only one predictor, Age, is statistically significant, and the others are not. What is likely going on among the four predictors? If you include more than one of these predictors in the model, what are some problems that can result?

*After building a regression model and performing residual diagnostics, you notice that the errors show severe departures from normality and appear to have nonconstant variance. What steps would you take in this case to resolve the errors? If the problems are not corrected after all steps are taken, what does that imply about the modeling approach you are taking? Explain in detail.*

**QUESTION 2-**Do you have a similar assignment and would want someone to complete it for you? Click on

the ORDER NOW option to get instant services at LindasHelp.com. We assure you of a well

written and plagiarism free papers delivered within your specified deadline.

AD:

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