An online retailer examined their transactional database to see how the value of total annual purchases ($) for individual customers was related to their annual income ($). They obtained the following regression model: Total annual purchases = -49.80 + 0.0246(annual income) correlation = 0.533 (a) What does the slope tell us? (Annual Income/ Total Annual Purchases) is/are predicted to increase by ($0.0246 / -$49.80) for each additional $1 of (Annual Income/ Total Annual Purchases). (b) What does the intercept tell us? A.The intercept does not have a practical meaning in this context. B. Total annual purchases are predicted to be $0.0246 when annual income = 0. C. Total annual purchases are predicted to be $-49.80 when annual income = 0. D. Annual income is predicted to be $0.0246 when total annual purchases = 0. E. Annual income is predicted to be $-49.80 when total annual purchases = 0. (c) Which statement is correct concerning the quality of this model? A. 28.4% of the variability in annual income can be accounted for by total annual purchases. B. 53.3% of the variability in total annual purchases can be accounted for by annual income. C. 28.4% of the variability in total annual purchases can be accounted for by annual income. D. 53.3% of the variability in annual income can be accounted for by total annual purchases.
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
An online retailer examined their transactional database to see how the value of total annual purchases ($) for individual customers was related to their annual income ($). They obtained the following regression model:
Total annual purchases = -49.80 + 0.0246(annual income)
(a) What does the slope tell us?
(Annual Income/ Total Annual Purchases) is/are predicted to increase by ($0.0246 / -$49.80) for each additional $1 of (Annual Income/ Total Annual Purchases).
(b) What does the intercept tell us?
(c) Which statement is correct concerning the quality of this model?
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