1. Consumption of electric power each month in 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: X2 X3 X4 240 25 24 91 100 236 31 21 90 95 270 45 24 88 110 274 60 25 87 88 301 65 25 91 94 316 72 26 94 99 300 80 25 87 97 296 84 25 86 96 267 75 24 88 110 276 60 25 91 105 288 50 25 90 100 261 38 23 89 98 (a) Fit a multiple linear regression model to these data. (b) Estimate o?. (c) Compute the standard errors of the regression coefficients. (d) Predict power consumption for a month in which x1 = 75°F, x2 = 24 days, x3 = 90%, and x4 = 98 tons.
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.
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