Question

Larry Swattle, a local attorney, is interested in understanding the relationship between the outside temperature and his energy usage. Larry finds his electric bills for the last 24 months and records the electric consumption in kilowatt hours. He then uses the internet to find the average daily temperature in Fahrenheit for his city for those months. The data appear in the Electricity worksheet of the Chp 15 HW Problems Data Workbook on Moodle.

Fit the simple linear regression model using monthly electric consumption as the dependent or Y variable and average daily temperature as the independent or X variable. Analyze the residuals to determine if they satisfy the three regression model assumptions.

Answer 1

To fit a simple linear regression model, collect the data, plot a scatter plot, calculate the line of best fit, and analyze the residuals.

Step-by-step explanation:

To fit a simple linear regression model using monthly electric consumption as the dependent variable and average daily temperature as the independent variable, you can follow these steps:

1. Collect the monthly electric consumption data (in kilowatt hours) and the average daily temperature data (in Fahrenheit) for the last 24 months.
2. Plot the data points on a scatter plot with average daily temperature on the x-axis and monthly electric consumption on the y-axis.
3. Calculate the line of best fit (regression line) that minimizes the distance between the data points and the line. This can be done using statistical software or by hand using least squares regression.
4. Analyze the residuals, which are the differences between the observed y-values and the predicted y-values from the regression line. The residuals should satisfy the three regression model assumptions: linearity, independence, and constant variance. This can be done by plotting the residuals against the predicted y-values and checking for any patterns or trends.