Simple Linear Regression Example and Analysis

Example of Simple Linear Regression in Real-World

1. Simple linear regression looks at the relationship between an independent and a dependent variable.

Give a real-world example of two variables that have this special relationship. Make sure that you answer the following questions:

(a) What is the independent (predictor) variable? Explain.

(b) What is the dependent (explanatory) variable? Explain.

(c) What is the nature of the independent and dependent variable relationship that you are exploring? Are we dealing with proportional or non-proportional behavior?

Explain. 2. Complete the following assignment: See attached Excel file that displays the relationship between the annual revenue in millions (x variable) and the current value in millions (y variable) of 30 professional basketball teams. Press SCATTERPLOT tab on bottom ribbon to see the data points and trendline. Return to DATA tab on bottom ribbon.

Change values in CURRENT VALUE column D to any 3 digit values you choose. Click SCATTERPLOT tab to see your datapoints and trendline. To find linear regression equation, right click any data point, click ADD A TRENDLINE. Scroll down to check boxes:

DISPLAY EQUATION, DISPLAY R-SQUARED VALUE (This is the coeffiecient of determination.) On your Excel sheet below your scatterplot,

(1) identify and interpret the slope of your equation

(2) identify and interpret the y-intercept of your equation

(3) identify and interpret the R-Squared value: what does it tell you about this relationship. For this part, you will need to attach an Excel file containing your scatterplot as well as regression results.

On your Excel sheet below your scatterplot you need to provide the following:

(a) Identify and interpret the slope of your equation. Make sure that you also provide the units associated with this measure. You must cast this discussion in a form which is relevant to the given application. That is, in terms of annual revenue (x-variable) and current value in millions (y-value).

(b) Identify and interpret the y-intercept of your equation. Make sure that you also provide the units associated with this measure. You must cast this discussion in a form which is relevant to the given application. That is, in terms of annual revenue (x-variable) and current value in millions (y-value).

(c) Write out your best-fit regression equation in terms of the given variables. Don’t just give me an equation in terms of y = mx + b. Example. If x = dosage of a drug (in mg) and y = heart rate (beats), your best fit regression equation might look like … Heart Rate = (10) * Dose + 55. The slope "10" tells us that heart rate will go up 10 beats for each 1 mg of the dose that is used. The y-intercept "55" tells us that heart rate equals 55 beats when zero mg of the dose is administered. It is the baseline or starting heart rate. Dose is in units of mg (milligrams) and heart rate is in units of beats.

(d) Identify and interpret the r-squared value. What does it tell you about this relationship? What does the percent value for r-squared tell us? Make sure that you identify the independent (predictor) and dependent (explanatory) variable within your example. Also, discuss why you have given them this designation.

(e) Although not explicitly asked for within the original instructions, the square root of r-squared gives us r. This is the correlation coefficient. What does the magnitude and sign of r tell us about how well the data lines up along a straight line on our scatterplot. Hint: r-squared tells us how well our regression equation fits the data, whereas r tells us how well our data lines up along a straight line.