Consumer Research is an independent agency that conducts research on consumer attitudes and behaviours for a variety of firms. In one study, a client asked for an investigation on consumer characteristics that can be used to predict the amount charged by credit card users. Data were collected on annual income (Income, $1000), household size (Size), and annual amount of credit charged to the credit card (Credit, $) for a random sample of 50 customers. These data are saved in the a3e2.xlsx file.
(a) For each of the three variables, answer the following questions. Is the variable qualitative or quantitative? If it is qualitative, is it ranked or unranked? If it is quantitative, is it discrete or continuous? What is its level of measurement? Explain your answers.
(b) Consider the following two pairs of variables: Credit and Income, and Credit and Size. In each case, do you expect the variables to be related to each other? If yes, do you expect the relationship to be positive or negative. Explain your answers.
(c) Using R, calculate the Pearson or Spearman correlation coefficient, whichever is more appropriate, for the two pairs of variables in part (b). In each case, briefly explain your choice between the Pearson and Spearman correlation coefficients and comment on the direction and relative strength of the relationship as implied by the point estimate.
(d) Based on your answers in part (b), perform an appropriate test with R at the 5% significance level on each pair of variables to determine whether there is a linear, or at least monotonic, relationship between the variables in the expected direction. In each case, show the hypotheses and state the statistical decision and the conclusion.