Project Part C: Regression and Correlation AnalysisUsing MINITAB perform the regression and...

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Project Part C: Regression and Correlation AnalysisUsing MINITAB perform the regression and correlation analysis for the data on CREDIT BALANCE (Y) and SIZE (X) by answering the following.
Generate a scatterplot for CREDIT BALANCE vs. SIZE, including the graph of the "best fit" line. Interpret.Determine the equation of the "best fit" line, which describes the relationship between CREDIT BALANCE and SIZE.Determine the coefficient of correlation. Interpret.Determine the coefficient of determination. Interpret.Test the utility of this regression model (use a two tail test with =.05). Interpret your results, including the p-value.Based on your findings in 1-5, what is your opinion about using SIZE to predict CREDIT BALANCE? Explain.Compute the 95% confidence interval for beta-1 (the population slope). Interpret this interval.Using an interval, estimate the average credit balance for customers that have household size of 5. Interpret this interval.Using an interval, predict the credit balance for a customer that has a household size of 5. Interpret this interval.What can we say about the credit balance for a customer that has a household size of 10? Explain your answer.In an attempt to improve the model, we attempt to do a multiple regression model predicting CREDIT BALANCE based on INCOME, SIZE and YEARS.
Using MINITAB run the multiple regression analysis using the variables INCOME, SIZE and YEARS to predict CREDIT BALANCE. State the equation for this multiple regression model.Perform the Global Test for Utility (F-Test). Explain your conclusion.Perform the t-test on each independent variable. Explain your conclusions and clearly state how you should proceed. In particular, which independent variables should we keep and which should be discarded.Is this multiple regression model better than the linear model that we generated in parts 1-10? Explain.All DeVry University policies are in effect, including the plagiarism policy.Project Part C report is due by the end of Week 7.Project Part C is worth 100 total points. See grading rubric below.Summarize your results from 1-14 in a report that is three pages or less in length and explains and interprets the results in ways that are understandable to someone who does not know statistics.
Submission: The summary report + all of the work done in 1-14 (Minitab Output + interpretations) as an appendix.
Format:
Summary ReportPoints 1-14 addressed with appropriate output, graphs and interpretations. Be sure to number each point 1-14.

Robert · Accepted Answer

Linear Regression Model
The output of linear regression as obtained in Minitab is shown below.
Regression Analysis: Income ($1,000) versus Credit Balance($)
The regression equation is 
Income ($1,000) = - 3.52 + 0.0119 Credit Balance($)
Predictor              Coef   SE Coef      T      P 
Constant             -3.516     5.483  -0.64  0.524 
Credit Balance($)  0.011926  0.001289   9.25  0.000
S = 8.40667   R-Sq = 64.1%   R-Sq(adj) = 63.3%
Analysis of Variance
Source          DF      SS      MS      F      P 
Regression       1  6052.7  6052.7  85.65  0.000 
Residual Error  48  3392.3    70.7 
Total           49  9445.0
Unusual Observations
         Credit    Income 
Obs  Balance($)  ($1,000)    Fit  SE Fit  Residual  St Resid 
  2        2047     25.00  20.90    2.96      4.10      0.52 X 
  4        3913     26.00  43.15    1.23    -17.15     -2.06R
R denotes an observation with a large standardized residual. 
X denotes an observation whose X value gives it large leverage.
1. Scatterplot for income ($1,000) versus credit balance($) 
The scatter plot between Income and credit balance is shown below.
As is evident from the scatter plot, there is a clear and definite relationship 
between the two variables. The variables Income and Credit Balance 
exhibit a strong linear positive relationship or correlation. If Credit 
balance increases, the income also increases.
60005000400030002000
80
70
60
50
40
30
20
Credit Balance($)
In
c
o
m
e
 (
$
1
,0
0
0
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Linear
Linear
Fits
Scatterplot of Income ($1,000) vs Credit Balance($)
2. Equation of the best fit line 
The equation of best fit line as obtained from Regression analysis is shown 
below. 
Income ($1,000) = - 3.52 + 0.0119 Credit_Balance($) 
Here, value of intercept (-3.52) implies the initial value of income, when 
credit balance is $ 0. The value of slope implies that with a unit increase in 
credit balance, there is 0.0119 units ($ 1,000) increase in income.
3. Coefficient of correlation 
Coefficient of correlation = sqrt (coefficient of determination) 
   = sqrt (0.641) 
   = 0.800625 
This implies that the variables Income and Credit Balance exhibit a strong 
linear positive relationship or correlation. If Credit balance increases, the 
income also increases.
4. Coefficient of determination 
Coefficient of determination = 64.1%, that is 64.1% variation in the 
dependent variable which is income is explained by the independent 
variable which is credit balance.
5. Utility of this regression model  
Null Hypothesis, Ho: Model is not significant 
Alternative Hypothesis, H1:

Project Part C: Regression and Correlation Analysis Using MINITAB perform the regression and correlation analysis for the data on CREDIT BALANCE (Y) and SIZE (X) by answering the following. Generate a...

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