Let Yt be the sales during month t (in thousands of dollars) for a photography studio, and let Pt be the price charged for portraits during month t. The data are in the file Week 4 Assignment Chapter 12 Problem 64. Use regression to fit the following model to these data: Yt = a + b1Yt−1 + b2Pt + et This equation indicates that last month’s sales and the current month’s price are explanatory variables. The last term, et, is an error term. If the price of a portrait during month 21 is $10, what would you predict for sales in month 21? Sales Price $400,000 $15 $1,042,000 $12 $1,129,000 $24 $1,110,000 $18 $1,336,000 $18 $1,363,000 $30 $1,177,000 $27 $603,000 $24 $582,000 $36 $697,000 $27 $586,000 $24 $673,000 $27 $546,000 $30 $334,000 $33 $27,000 $24 $76,000 $27 $298,000 $30 $746,000 $18 $962,000 $21 $907,000 $24
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.
Let Yt be the sales during month t (in thousands of dollars) for a photography studio, and let Pt be the price charged for portraits during month t. The data are in the file Week 4 Assignment Chapter 12 Problem 64. Use regression to fit the following model to these data:
Yt = a + b1Yt−1 + b2Pt + et
This equation indicates that last month’s sales and the current month’s price are explanatory variables. The last term, et, is an error term.
- If the price of a portrait during month 21 is $10, what would you predict for sales in month 21?
| Sales | Price |
| $400,000 | $15 |
| $1,042,000 | $12 |
| $1,129,000 | $24 |
| $1,110,000 | $18 |
| $1,336,000 | $18 |
| $1,363,000 | $30 |
| $1,177,000 | $27 |
| $603,000 | $24 |
| $582,000 | $36 |
| $697,000 | $27 |
| $586,000 | $24 |
| $673,000 | $27 |
| $546,000 | $30 |
| $334,000 | $33 |
| $27,000 | $24 |
| $76,000 | $27 |
| $298,000 | $30 |
| $746,000 | $18 |
| $962,000 | $21 |
| $907,000 | $24 |
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