Minitab Assignment due Tues Nov 10

Please word-process your answers to these questions, copy/pasting relevant, well-labeled Minitab output into a Word file as appropriate. When you are asked to comment, please write in complete sentences.

The Minitab worksheet utilities.mtw contains data collected by a homeowner on the monthly energy usage of his home between September of 1990 and May of 1997. Average temperature is recorded in degrees Fahrenheit, gas usage is recorded in therms per day, and electricity usage is recorded in kilowatt hours per day. One of the homeowners goals was to investigate how well average temperature could be used to predict gas usage and/or electricity usage.

a) What are the observational units with these data?

b) Produce (and submit) a scatterplot of gas usage vs. average temperature. Also produce (and submit) a scatterplot of electricity usage vs. average temperature. Comment on the direction, strength, and form of the association as revealed in each scatterplot.

c) For which response variable (gas usage or electricity usage) is average temperature a better predictor? Explain.

d) Use Minitab to determine the regression line for predicting gas usage from average temperature. Report the equation of this line, and also submit a scatterplot with the line superimposed. (Stat> Regression> Fitted line plot.)

e) Use this regression line to predict the gas usage in a month for which the average temperature is 45 degrees. (When you finish the calculation, look at the scatterplot and line to make sure that your answer is reasonable.)

f) Determine the residual value for November of 1990.

g) Based on the scatterplot (with the regression line drawn on it) alone, circle the point corresponding to the month with the largest positive residual. Also identify which month this is.

h) Write a sentence interpreting the value of the slope coefficient in this context.

i) What proportion of the variability in monthly gas usage is explained by the least squares line with average temperature?

j) What proportion of the variability in monthly electricity usage is explained by the least squares line with average temperature?