A market analyst is studying sales figures for two competing products, Alpha and Beta. In the accompanying table, A represents the annual sales of Alpha, in thousands of dollars, and B represents the annual sales of Beta, in thousands of dollars. Time t is measured in years since 2013. t 0 1 2 3 A 8.80 9.06 9.34 9.62 B 2.40 3.07 3.93 5.03 (a) Use exponential regression to find models for A and B. (Round regression parameters to two decimal places.) model for A: A = 9.62 × 0.97t A = 8.80 × 1.03t A = 5.23 × 1.24t A = 12.62 × 0.85t A = 9.21 × 1.15t model for B: B = 2.40 × 1.28t B = 5.03 × 0.72t B = 9.21 × 0.93t B = 1.23 × 1.54t B = 3.61 × 1.15t (b) By what annual percentage are sales for Alpha growing? (Use the model found in part (a).) % By what annual percentage are sales for Beta growing? (Use the model found in part (a).) %
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.
A market analyst is studying sales figures for two competing products, Alpha and Beta. In the accompanying table, A represents the annual sales of Alpha, in thousands of dollars, and B represents the annual sales of Beta, in thousands of dollars. Time t is measured in years since 2013.
| t | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| A | 8.80 | 9.06 | 9.34 | 9.62 |
| B | 2.40 | 3.07 | 3.93 | 5.03 |
model for A:
model for B:
(b) By what annual percentage are sales for Alpha growing? (Use the model found in part (a).)
%
By what annual percentage are sales for Beta growing? (Use the model found in part (a).)
%
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