Simple Regression INSTRUCTIONS: Use MINITAB 17 to complete the following questions. You are to work independently on this assignment. All data sets for this assignment have been provided. Please...

Simple Regression
INSTRUCTIONS: Use MINITAB 17 to complete the following questions. You are to work
independently on this assignment. All data sets for this assignment have been provided.
Please submit your completed assignment that includes relevant MINITAB output and
comments (make sure to comment on your results when asked) as ONE WORD document.
1. Use the data set EnergyConsumption.MTW. These data represent annual usage of
renewable energy sources (trillion BTUs). Usage data are provided for three renewable sources
of energy (wind, geothermal and biomass). You are interested in forecasting annual wind energy
usage.

(a) Fit a simple regression model using annual geothermal usage as the independent variable.
Is the regression equation significant? Explain your answer.
Regression Analysis: Wind versus Geothermal

Method
Rows unused 10
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Regression 1 161974 161974 6.46 0.018
Geothermal 1 161974 161974 6.46 0.018
Error 25 627252 25090
Total 26 789226
Model Summary
S R-sq R-sq(adj) R-sq(pred)
158.398 20.52% 17.34% 7.13%
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant -264 149 -1.77 0.089
Geothermal 1.224 0.482 2.54 0.018 1.00
Regression Equation
Wind = -264 + 1.224 Geothermal
The regression model is significant as the p-value of the ANOVA test is less than the level of
significance 0.05.
(b) How much of the variability in annual wind energy usage can be explained by annual
geothermal usage?
20.52% of the variability in annual wind energy usage can be explained by annual geothermal
usage.
(c) Construct and evaluate all four residual plots (normal probability plot of residuals,
residuals versus fitted values, histogram of residuals and residuals versus order plot).


The normal probability plot and histogram suggest that the distribution of residuals deviates from
normal distribution i.e. the residuals do not follow normal distribution. Also there is no such
specific pattern in relation of residuals with fitted values.
(d) Construct the ACF and PACF of residuals. Interpret.


Both ACF and PACF of residuals suggest that residuals have significant spike at lag one in both
ACF and PACF graph which is typical for autoregressive moving average process of order one.
(e) Suggest how the model might be improved (based on the residual plots).
The log transformation or box-cox transformation may be useful to make the model normally
distributed and the model might be improved.
2. Use the data set TigerTransport.MTW.These data represent cargo weight (1000s of
pounds) and MPG (miles per gallon) for a sample of trips made by Tiger Transport.
(a) Fit a simple regression model to predict MPG using cargo weight as the independent
variable. Is the regression equation significant? Explain...