Use Regression with One Predictor | JMP 13.2

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Discovering JMP • Analyze Your Data • Analyze Relationships • Use Regression with One Predictor

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Use Regression with One Predictor

This example uses the Companies.jmp data table, which contains financial data for 32 companies from the pharmaceutical and computer industries.

Intuitively, it makes sense that companies with more employees can generate more sales revenue than companies with fewer employees. A data analyst wants to predict the overall sales revenue for each company based on the number of employees.

To accomplish this task, do the following:

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Discover the Relationship

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Fit the Regression Model

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Predict Average Sales

Discover the Relationship

First, create a scatterplot to see the relationship between the number of employees and the amount of sales revenue. This scatterplot was created in Create the Scatterplot in Visualize Your Data. After hiding and excluding one outlier (a company with significantly more employees and higher sales), the plot in Scatterplot of Sales ($M) versus # Employ shows the result.

Scatterplot of Sales ($M) versus # Employ

This scatterplot provides a clearer picture of the relationship between sales and the number of employees. As expected, the more employees a company has, the higher sales that it can generate. This visually confirms the data analyst’s guess, but it does not predict sales for a given number of employees.

Fit the Regression Model

To predict the sales revenue from the number of employees, fit a regression model. From the red triangle for Bivariate Fit, select Fit Line. A regression line is added to the scatterplot and reports are added to the report window.

Regression Line

Within the reports, look at the following results:

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the p-value of <.0001

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the RSquare value of 0.618

From these results, the data analyst can conclude the following:

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The p-value is less than the significance level of 0.05. Therefore, including the number of employees in the prediction model significantly improves the ability to predict average sales.

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Since the RSquare value in this example is large, this confirms that a prediction model based on the number of employees can predict sales revenue. The RSquare value shows the strength of a relationship between variables, also called the correlation. A correlation of 0 indicates no relationship between the variables, and a correlation of 1 indicates a perfect linear relationship.

Predict Average Sales

Use the regression model to predict the average sales a company might expect if they have a certain number of employees. The prediction equation for the model is included in the report:

Average sales = 1059.68 + 0.092*employees

For example, in a company with 70,000 employees, the equation is as follows:

$7,499.68 = 1059.68 + 0.092*70,000

In the lower right area of the current scatterplot, there is an outlier that does not follow the general pattern of the other companies. The data analyst wants to know whether the prediction model changes when this outlier is excluded.

Exclude the Outlier

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Click on the outlier.

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Select Rows > Exclude/Unexclude.

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Fit this model by selecting Fit Line from the red triangle menu for Bivariate Fit.

The following are added to the report window (see Comparing the Models):

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a new regression line

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a new Linear Fit report, which includes:

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a new prediction equation

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a new RSquare value

Comparing the Models

Interpret the Results

Using the results in Comparing the Models, the data analyst can make the following conclusions:

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The outlier was pulling down the regression line for the larger companies, and pulling the line up for the smaller companies.

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The new model fits the data better, since the new RSquare value (0.88) is closer to 1 than the first RSquare value (0.618).

Draw Conclusions

Using the new prediction equation, the predicted average sales for a company with 70,000 employees can be calculated as follows:

$8961.37 = 631.37 + 0.119*70,000

The prediction for the first model was $7499.68, so this model predicts a higher sales total by $1461.69.

The second model, after removing the outlier, describes and predicts sales totals based on the number of employees better than the first model. The data analyst now has a good model to use.

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Help created on 9/19/2017