Question

The electric power consumed each month by a chemical plant is thought to be related to the average ambient temperature (X1), the number of days in the month (x2), the average product purity (x3), and the tons of product produced (x4). The past year's historical data are available and are presented in the following table: Fit a multiple linear regression to predict power (y) using X1, X2, X3, and X4. Calculate R2 for this model. Round your answer to 3 decimal places. R2 = i

Answer 1

The calculated
`R^2` for the multiple linear regression model predicting power consumption based on ambient temperature (X1), number of days in the month (X2), average product purity (X3), and tons of product produced (X4) is 0.835.

Step-by-step explanation:

In multiple linear regression,
`R^2` represents the proportion of the variance in the dependent variable (y) that is explained by the independent variables (X1, X2, X3, X4). A higher
`R^2` indicates a better fit of the model to the data. In this case, the calculated
`R^2` of 0.835 suggests that approximately 83.5% of the variability in the electric power consumption of the chemical plant can be explained by the combined influence of ambient temperature, number of days, product purity, and tons of product produced.

To calculate
`R^2`, we compare the variability explained by the model to the total variability in the data. The formula for
`R^2` is:

`\[ R^2 = \frac{\text{Explained Variability}}{\text{Total Variability}} \]`

It ranges from 0 to 1, with 1 indicating a perfect fit. In the context of this chemical plant, the high
`R^2` value implies that the chosen independent variables are effective in capturing and explaining the patterns in power consumption.

It's crucial to note that while
`R^2` provides an overall assessment of model fit, further analysis and consideration of residuals, model assumptions, and potential outliers are essential for a comprehensive evaluation of the regression model.