Reference no: EM133069762
The purpose of this assessment is to understand how balance on credit cards relates to various characteristics of the user (income, age, years of education, gender, whether a student or not, marital status, ethnicity, and credit rating) as well as of the credit cards themselves (total credit limit and the number of cards, in addition to balance). Assume that the currency is US dollars (assume income is in thousand of US dollars per year).
For each of the questions below, use one or more of the following statistical concepts: one-sample t-test, two-sample t-test, analysis of variance, correlation, simple linear regression, multiple linear regression. Be quantitative in your answers. Set up an appropriate hypothesis test and conclude from a p-value, or calculate a correlation coefficient or the linear regression equation. Use appropriate plots to support your answers.
-A company manager says that the average balance on their credit cards is $500. Do you think that this assertion is justified? Use a one-sample t-test to draw your conclusion.
-Is there a difference between men and women as far as average balance is concerned? Use a two-sample t-test to draw your conclusion.
-Is there a difference between students and non-students as far as average balance is concerned? Use a two-sample t-test to draw your conclusion.
-It is generally assumed that if there are more credit cards then the balance on the cards will be more. Based on this dataset, do you think this is true? Calculate a correlation coefficient and show a scatter plot to support your answer.
-Examine whether the following demographic variables influence balance: (a) age, (b) years of education, (c) marital status. For age and years of education, use scatter plots to depict their relationship with balance and calculate the correlation coefficient. For the relationship between marital status and balance, use a two-sample t-test to draw your conclusion
-"Ethnicity of the cardholder does not matter as far a balance is concerned." Carry out an analysis of variance (ANOVA) and discuss whether this statement is supported by the data or not.
-A general principle that credit card companies often follow is to assign a higher credit limit to people with a higher credit rating. Does the data show that this principle is being followed?
-Run a simple linear regression of balance on the credit limit. (Here credit limit is the X and the balance is the Y). Report the coefficients and the R-squared. Show a scatter plot.
-Run a simple linear regression of balance (Y) on credit rating (X). Report the coefficients and R-squared. Show a scatter plot
-Consider your findings in questions 8-9. Discuss business mechanisms to increase or decrease the balance on credit cards. Try to quantify your answers.In this context, focus on possible specific strategies using variables in Q8 and Q9 that the business could adopt to increase the balance on credit cards
-The credit limit is provided as a consolidated amount for all the credit cards the cardholder has. Run a multiple linear regression of Balance (Y) on Limit and Cards as two X variables. Report the coefficients. Discuss the effect on the balance of (a) increasing the credit limit on the same number of cards and (b) increasing the number of cards without altering the total credit limit.
-Run a simple linear regression equation with Income as X and Balance as Y. Report the coefficients. Is the coefficient of Income significantly different from zero? What does this say about the effect of income on balance?
-Based on the equation derived in question 12, what is the estimated balance for a person with an income of USD 100k per year?
-Based on the dataset, explore the relationship between credit card balance (Y) and (a) Income (b) Age (c) Education (c) Limit, and (d) Rating as X variables? Estimate a multiple linear regression model and report the statistical significance of each of these variables.