Question

# Install the R package SemiPar to get access to the elec.temp data...

Install the R package SemiPar to get access to the elec.temp data set for electricity usage vs temperature (in Farenheit) in a house1 . Using R but not the lm command in R, do the following.

(a) Perform a simple linear regression using temperature as the predictor variable and the logarithm of the electricity usage as the response. Find the least square estimate for the coefficients.

(b) Conduct a hypothesis test (via a t-test) to test whether electricity usage is associated with the temperature in the house. Use a significance level of 0.05 for the test. What is the p-value of this test?

(c) Construct a prediction interval for the electricity usage when the temperature is 70 degrees Farenheit

and 40 degrees Farenheit.

(d) Compute SSE, SSR and SST o and repeat part (b) using an F-test. Would you expect the results to be the same or different? What is the p-value? Is there a difference in using a t-test as opposed to an

F-test?

(e) Find the 95% confidence band for the regression line using the Working-Hotelling approach and plot

it together with the data scatter plot and the least-squares line.

Image transcription text

Exercise 5: (15 pts) Install the R package SemiPar to get access to the elec.temp data set for electricity usage vs temperature (in Farenheit) in a house . Using R but not the Im command in R, do the following. (a) Perform a simple linear regression using temperature as the predictor variable and the logarithm of the electricity usage as the response. Find the least square estimate for the coefficients. (b) Conduct a hypothesis test (via a t-test) to test whether electricity usage is associated with the tem- perature in the house. Use a significance level of 0.05 for the test. What is the p-value of this test? (c) Construct a prediction interval for the electricity usage when the temperature is 70 degrees Farenheit and 40 degrees Farenheit. (d) Compute SSE, SSR and SSTo and repeat part (b) using an F-test. Would you expect the results to be the same or different? What is the p-value? Is there a difference in using a t-test as opposed to an F-test? (e) Find the 95% confidence band for the regression line using the Working-Hotelling approach and plot it together with the data scatter plot and the least-squares line.

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