# Regression Equations and Meanings

Scenario: Regression equations are created by modeling data, such as the following:

Sales = (Cost Per Item - Number of Items) - Constant Charges

In this equation, constant charges may be rent, salaries, or other fixed costs. This includes anything that you have to pay for periodically as a business owner. This value is negative because this cost must be paid each period and must be paid whether you make a sale or not.

Your company may wish to release a new e-reader device. Based on data collected from various sources, your company has come up with the following regression equation for the sales of the new e-reader:

Sales = $0.15 - number of e-readers sold - $28

Or, assuming x = the number of e-readers sold, this would be the same regression equation:

Sales = 0.15x - 28

In this case, the values are given in thousands (i.e., the cost of making an individual e-reader will be $150 [0.15 - 1,000], with $28,000 [28 * 1,000] in constant charges).

Answer the following questions based on the given regression equation:

1.Using the graphing program that you downloaded from www.padowan.dk/graph, graph the sales equation. Discuss the meaning of the x- and y-axis values on the graph. (Hint: Label the axis with the Text tool in the graphing program.)

2.Based on the results of the graph and the sales equation provided, discuss the relationship between sales and number of e-readers produced. (Hint: Consider the slope and y-intercept.)

3.If the company does not sell a single e-reader, how much is lost in sales? Mathematically, what is this value called in the equation?

4.If the company sells 5,000 e-readers, how much will the company make (or lose) in sales?

5.If sales must equal 100 thousand, how many e-readers will your company need to sell? (Round up to the nearest e-reader.)

6.If your company is hoping to break even, how many e-readers will need to be sold to accomplish this? (Round up to the nearest e-reader.)

© BrainMass Inc. brainmass.com October 25, 2018, 4:30 am ad1c9bdddfhttps://brainmass.com/math/interpolation-extrapolation-and-regression/regression-equations-and-meanings-381207

#### Solution Summary

Sale costs of a company is examined. Regression analysis is used to calculate the sales goals of e-readers.

Houston weather data: regression equation, R-squared, intercept meaning

Instructions:

? Write the regression equation

? What does R-squared value tell you?

? What meaning does intercept have?

? Which is warmer, a day with rain or a day without?

? Is KIAH_Precip a good predictor?

? Describe fit of regression

It might be supposed that rainy days would tend to be cooler than days without rain, other factors being equal. Furthermore, if that rain is widespread enough to affect more than one reporting station in a city, the effect might be expected to be even more pronounced.

The following output from the Excel Analysis ToolPak, shows a regression analysis on a year of Houston weather data. Precipitation data were collected for George Bush International Airport (KIAH) and for Hobby Airport (KHOU), coded as 1 for precipitation and 0 for no precipitation. These values were used as "binary predictors". The dependent variable is the departure of the daily high temperature from the 30 year normal for the date. So, for example, a day with a high temperature two degrees below normal would be shown as a departure value of -2.0.

Regression Statistics

Multiple R 0.1768

R Square 0.0313

Adjusted R Square 0.0258

Standard Error 6.8608

Observations 360

ANOVA

df SS MS F Significance F

Regression 2 542.19 271.10 5.7594 0.0035

Residual 357 16804.16 47.07

Total 359 17346.35

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%

Intercept 2.6668 0.4381 6.0878 0.0000 1.8053 3.5283

KIAH_Precip -2.3840 1.0423 -2.2873 0.0228 -4.4337 -0.3342

KHOU_Precip -0.6236 0.9994 -0.6240 0.5331 -2.5890 1.3419

a) Write the fitted regression equation

b) What does the R-squared value tell you?

c) What, if any, meaning does the intercept have?

d) Other things being equal, is the temperature warmer on days with or without rain at KIAH?

e) Does the 95% confidence interval for KIAH_Precip slope give us any confidence that precip vs. no precip at KIAH is an important predictor of temperature?