The number of pounds of steam used per month by a chemical plant is thought to be related to the average ambient temperature (in F) for that month. The past year’s usage and temperatures are in the following table: Assuming that a simple linear regression model is appropriate, fit the regression model relating stem usage (y) to the average temperature (x). What is the estimate of Sigma2? What is the estimate of expected stem usage when t
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.
- The number of pounds of steam used per month by a chemical plant is thought to be related to the average ambient temperature (in F) for that month. The past year’s usage and temperatures are in the following table:
- Assuming that a simple linear regression model is appropriate, fit the regression model relating stem usage (y) to the average temperature (x). What is the estimate of Sigma2?
- What is the estimate of expected stem usage when the average temperature is 55 F?
- What change in
mean stem usage is expected when the monthly average temperature changes by 1 F? - Suppose that the monthly average temperature is 47 F. Calculate the fitted value of y and the corresponding residual.
- Test for significance of regression using α=0.01 (Use ANOVA).
- Calculate the r2 of the model.
- Find a 99% CI for B1 .
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Let Y represent the steam usage per month by the chemical plant, and X represent the average ambient temperature for the month.
| X | Y | X2 | Y2 | XY |
| 21 | 185.79 | 441 | 34517.92 | 3901.59 |
| 24 | 214.47 | 576 | 45997.38 | 5147.28 |
| 32 | 288.03 | 1024 | 82961.28 | 9216.96 |
| 47 | 424.84 | 2209 | 180489 | 19967.48 |
| 50 | 454.58 | 2500 | 206643 | 22729 |
| 59 | 539.03 | 3481 | 290553.3 | 31802.77 |
| 68 | 621.55 | 4624 | 386324.4 | 42265.4 |
| 74 | 675.06 | 5476 | 455706 | 49954.44 |
| 62 | 562.03 | 3844 | 315877.7 | 34845.86 |
| 50 | 452.93 | 2500 | 205145.6 | 22646.5 |
| 41 | 369.95 | 1681 | 136863 | 15167.95 |
| 30 | 273.98 | 900 | 75065.04 | 8219.4 |
| ΣX=558 | ΣY=5062.24 | ΣX2=29256 | ΣY2=2416144 | ΣXY=265864.6 |
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