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# Scatter Plots with Trendline

1. Open Customer Data.xlsx. Click Sheet 1 Tab. Click SigmaXL > Graphical Tools > Scatter Plots; if necessary, click Use Entire Data Table, click Next.

2. Select Overall Satisfaction, click Numeric Response (Y) >>; select Avg Days Order Time to Delivery, click Numeric Predictor (X1) >>. Check Trendline, 95% Confidence Interval and 95% Prediction Interval as shown:

3. Click OK. The resulting Scatter Plot is shown with equation, trendline, 95% confidence interval (blue lines – for a given X value this is the 95% confidence interval for predicted mean Overall Satisfaction) and 95% prediction interval (red lines – for a given X value this is the 95% confidence interval for predicted individual values of Overall Satisfaction).

The equation is based on linear regression, using the method of least squares. R-squared * 100 is the percent variation of Y explained by X (here 10.3%).

4. Now we want to redo the Scatter Plot and stratify by Customer Type. Press F3 or click Recall SigmaXL Dialog to recall last dialog. (Or, Click Sheet 1 Tab; Click SigmaXL > Graphical Tools > Scatter Plots; click Next.)

5. Select Overall Satisfaction, click Numeric Response (Y) >>; select Average Days Order Time to Delivery, click Numeric Predictor (X1) >>; select Customer Type, click Group Category (X2) >>, Uncheck 95% Confidence Interval and 95% Prediction Interval. Click OK:

Clearly, according to the analysis, Customer Type 3 is happier if orders take longer! But, does this make sense? Of course not! Customer Sat scores should not increase with Order to Delivery time. What is happening here? This is a coincidental situation. Something else is driving customer satisfaction. Later, we will look at the Scatter Plot Matrix to help us investigate other factors influencing Customer Satisfaction.

Tip: Be careful when interpreting scatter plots (and other statistical tools): Y versus X correlation or statistical significance does not always mean that we have a causal relationship. Umbrella sales are highly correlated to traffic accidents, but we cannot reduce the rate of traffic accidents by purchasing fewer umbrellas! The best way to validate a relationship is to perform a Design of Experiments (see Improve Phase).

# Scatter Plots with Quadratic Trendline

SigmaXL does not include nonlinear or polynomial curve fitting, so this example shows how a trendline in a Scatter Plot with Trendline may be modified in Excel to show a quadratic relationship.

1. Open Daily Electricity Demand with Predictors – ElecDaily.xlsx (Sheet 1 tab). This is daily electricity demand (GW) for the state of Victoria, Australia, every day during 2014. Temp (C) is the maximum daily temperature in degrees Celsius for the city of Melbourne. (The additional columns are not used here: TempSq is Temperature squared, WorkDay takes on the value 1 on work days and 0 otherwise. This data is analyzed later using Time Series Forecasting, see ARIMA Forecast with Predictors).

2. Click SigmaXL > Graphical Tools > Scatterplots. Ensure that the entire data table is selected. If not, check Use Entire Data Table. Click Next.

3. Select Demand, click Numeric Response (Y) >>; select Temp (C), click Numeric Predictor (X1) >>. Check Trendline.

4. Click OK. A Scatter Plot of Electricity Demand versus Temperature is produced.

5. This shows a quadratic relationship: high temperatures in the summer cause electricity demand for air conditioning, low temperatures in the winter cause demand for heating. We will modify the trendline in Excel to a quadratic fit. Click on the Trendline, right click and select Format Trendline as shown:

The Format Trendline options are given. Select Polynomial with Order 2 as shown.

6. The Trendline is now a quadratic function as shown:

7. P-Values for coefficients and model residuals are not available. For a quadratic model like this, these may be obtained using Multiple Linear Regression with Temp and TempSq as model predictors.

8. Nonlinear curve fitting may also be performed using Excel’s Solver. See, for example, this video tutorial by Taylor Sparks.

# Web Demos

Our CTO and Co-Founder, John Noguera, regularly hosts free Web Demos featuring SigmaXL and DiscoverSim