1) The local electric company wants to determine the relationship between electr
ID: 3153305 • Letter: 1
Question
1) The local electric company wants to determine the relationship between electricity consumption and the thermostat settings of customer water heaters. They collected data on the total electric consumption (in kilowatts) and the water heater thermostat settings (in degrees Fahrenheit) for 100 customers and they ran a regression on these data. Refer to the output from this regression (shown below) to answer the following:
l) What is the regression equation?
m) Interpret the coefficients of the regression equation.
n) What is the coefficient of correlation and what does it tell you?
o) What is the coefficient of determination and what does it tell you?
p) Say you want to run a test to determine if the slope of the regression line is truly different from 0. Specify
the test. What is the p-value for this test? Would you reject the null hypothesis at ? = .01? q) What does the P-value in the row for “Intercept” refer to and what does it tell you?
Explanation / Answer
l) What is the regression equation?
Total electric consumption = 6197.614218 + 14.98299168 (Water heater thermostat settings)
m) Interpret the coefficients of the regression equation.
When water heater thermostat setting is at 0 degrees Fahrenheit, average total electric consumption should be 6197.614218 kilowatts. Per degree Fahrenheit increase in water heater thermostat setting increases average total electric consumption by 14.98299168 kilowatts.
n) What is the coefficient of correlation and what does it tell you?
Since slope is positive, correlation must also be positive.
r = 0.1190791 = 0.345
This shows there is weak positive correlation between Water heater thermostat settings and Total electric consumption.
o) What is the coefficient of determination and what does it tell you?
r² = 0.1190791. This shows only 11.9% variation in Total electric consumption can be explained by linear relationship between Water heater thermostat settings and Total electric consumption.
p) Say you want to run a test to determine if the slope of the regression line is truly different from 0. Specify
the test. What is the p-value for this test? Would you reject the null hypothesis at = .01?
t test is used o determine if the slope of the regression line is truly different from 0. The test statistic is 3.63967288 and p-value is 0.00043802 which is less than = .01. We can conclude that there is sufficient evidence that the slope of the regression line is truly different from 0.
q) What does the P-value in the row for “Intercept” refer to and what does it tell you?
p-value is 3.3126E-19 which is less than = .01. We can conclude that there is sufficient evidence that the intercept is also significant.
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