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

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

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

1. Strength (in MPa): The compressive strength of the concrete.
2. Age (in days): The number of days the concrete was allowed to cured.
3. Coarse_Aggregate (in kg/m³): The proportion of coarse aggregate in the mix.
4. Fine_Aggregate (in kg/m³): The proportion of fine aggregate in the mix.
5. Cement (in kg/m³): The proportion of cement in the mix.
6. Slag (in kg/m³): The proportion of furnace slag in the mix.
7. Superplasticizer (in kg/m³): The proportion of plasticizer in the mix.
8. Water (in kg/m³): The proportion of water in the mix.
9. Ash (in kg/m³): The proportion of fly ash in the mix.

Part 1:

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

1. Strength (no transformation)
2. Square root of Strength
3. Squared Strength
4. (Natural) Log of Strength
5. Reciprocal of Strength

Part 2:

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

1. Use t-tests to determine if any of the predictors significantlyaffect the compressive strength of concrete. Explain why each variableshould or should not be included in the model. Assume α = 0.05. Show theappropriate model results to explain your answer.
2. 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 allthe remaining variables still statistically significant? Show theappropriate model results to explain your answer.
3. Based on the RM, should there be concern about multicollinearityamong the predictors selected? Show the appropriate model results toexplain your answer.
4. After fitting the RM, derive the residual plot (standardizedresiduals vs. standardized predicted values) and normal probabilityplot. Interpret each plot.
5. What is the coefficient of determination, R², of the RM? How would you interpret the R²?
6. Based on the RM, what would be the new estimated compressivestrength that is currently 50 MPa, after a 10-day increase in curingtime? Assume all other predictors are held constant.
7. How would you interpret the intercept (constant) in the RM? Does theinterpretation 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?

1. Age: 50 days
2. Coarse_Aggregate: 900 kg/m³
3. Fine_Aggregate: 600 kg/m³
4. Cement: 300 kg/m³
5. Slag: 200 kg/m³
6. Superplasticizer: 7 kg/m³
7. Water: 190 kg/m³
8. Ash: 70 kg/m³

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 priorto beginning the assignment to become familiar with the expectationsfor successful completion. PLEASE MAKE SURE THAT THE ASSIGNMENT INCLUDES THE FLOWING… Q-Q plot SPSS outputs for each transformation and selection of whichplot should be used to build a multiple linear model are complete andcorrect, 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 thenumber of minutes that 10- to18-year-old students spend on Twitter. Todo so, you build a linear regression model with Twitter usage (Y)measured as the number of minutes per week. The four predictors youinclude in the model are Height, Weight, Grade Level, and Age of eachstudent. You build four simple linear regression models with Yregressed separately on each predictor, and each predictor isstatistically significant. Then you build a multiple linear regressionmodel with Y regressed on all four predictors, but only one predictor,Age, is statistically significant, and the others are not. What islikely going on among the four predictors? If you include more than oneof these predictors in the model, what are some problems that canresult? QUESTION 2- After building a regression model and performing residual diagnostics,you notice that the errors show severe departures from normality andappear to have nonconstant variance. What steps would you take in thiscase to resolve the errors? If the problems are not corrected after allsteps are taken, what does that imply about the modeling approach youare taking? Explain in detail.