Dex Research Limited conducted a research to investigate consumer characteristics that can be used to predict the amount charged by credit card users. The following multiple regression output is based on a data collected by this research company on annual income, household size and annual credit card charges for a sample if 50 consumers. Regression Statistics Multiple R 0.9086 R Square A Adjusted R Square 0.8181 Standard Error 398.091 Observations B ANOVA df SS MS F Significance F Regression 2 C E G 1.50876E-18 Residual D 7448393 F Total 49 42699149 Coefficients Standard Error t Stat P-Value Intercept 1304.9048 197.6548 6.6019 3.28664E-08 Income ($1000s) 33.1330 3.9679 H 7.68206E-11 Household size 356.2959 33.2009 10.7315 3.12342E-14 a. Complete the missing entries from A to H in this output b. Estimate the annual credit card charges for a three-person household with an annual income of $40,000. c. Did the estimated regression equation provide a good fit to the data? Explain
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.
Dex Research Limited conducted a research to investigate consumer characteristics that can be used to predict the amount charged by credit card users. The following multiple regression output is based on a data collected by this research company on annual income, household size and annual credit card charges for a sample if 50 consumers.
| Regression Statistics | |||||
| Multiple R | 0.9086 | ||||
| R Square | A | ||||
| Adjusted R Square | 0.8181 | ||||
| Standard Error | 398.091 | ||||
| Observations | B | ||||
| ANOVA | |||||
| df | SS | MS | F | Significance F | |
| Regression | 2 | C | E | G | 1.50876E-18 |
| Residual | D | 7448393 | F | ||
| Total | 49 | 42699149 | |||
| Coefficients | Standard Error | t Stat | P-Value | ||
| Intercept | 1304.9048 | 197.6548 | 6.6019 | 3.28664E-08 | |
| Income ($1000s) | 33.1330 | 3.9679 | H | 7.68206E-11 | |
| Household size | 356.2959 | 33.2009 | 10.7315 | 3.12342E-14 |
a. Complete the missing entries from A to H in this output
b. Estimate the annual credit card charges for a three-person household with an annual income of $40,000.
c. Did the estimated regression equation provide a good fit to the data? Explain
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