Electricity Usage

Step 1: Graph of Usage by Temperature shows some hint of a non-linear relationship. The Residual vs. Fits plot confirms this

Linear model is bad, so go on

Step 2: Transformations

Square root model, bad
Exponential model, good, R²=80.6%
Power model, good, R²=81.1%

Step 3: Polynomial Model

Model p-value of highest order term

Quadratic 0.000

Cubic 0.752

so the best polynomial model is the quadratic. It has R²=84.7%

Step 4: Best Model
good model with highest R² is quadratic, so that is our final choice.

How do the good models compare? One way to do this is to draw the fitted line plot with all of the lines on it. Here is how this looks:

and here is how this graph is done:
Start with Graph > Scatterplot > Simple, Response=Usage, Predictor=Temperature
Using Stat > Basic Statistics > Display Descriptive Statistics, Variable= Temperature we see that Temperature has values from 24 to 79. We make a new column with Calc > Make Patterned Data > Simple set of numbers, Store Patterned data in: NewTemp, From first value=24 , To last value=79 , in steps of=1
Calculate the fitted values for the three models as follows
Calc > Calculator, Store in: FitExp, Expression: 207.5 * 10**(-0.0138*NewTemp)
Calc > Calculator, Store in: FitPower, Expression: 20320*NewTemp**(-1.6)
Calc > Calculator, Store in: FitQuad, Expression:196.7 - 4.640 * Temperature + 0.03073 * Temperature**2

right-click graph, Add > Calculated Line, y=FitExp, x=NewTemp. Select line, right-click, Edit Line, change size to 2 and color to blue
Repeat for FitPower and FitQuad
select y-axis, right-click, select Edit y sacle, uncheck maximum, type 130

Click on the line icon above the graph, draw short line in upper right corner, select line, change size to 2 and color to blue. Click on T icon, add text next to line, change font size to 8.
Repeat for other lines
Click on box icon, draw box around legend, select box, right-click, choose Edit Rectangle, Custom Type: N