How to Analyze the Regression Analysis Output from Excel

In a simple regression model, we are trying to determine if a variable Y is linearly dependent on variable X. That is, whenever X changes, Y also changes linearly. A linear relationship is a straight line relationship. In the form of an equation, this relationship can be expressed as

Y = α + βX + e

In this equation, Y is the dependent variable, and X is the independent variable. α is the intercept of the regression line, and β is the slope of the regression line. e is the random disturbance term.

The way to interpret the above equation is as follows:

Y = α + βX (ignoring the disturbance term “e”)

gives the average relationship between the values of Y and X.

For example, let Y be the cost of goods sold and X be the sales. If α = 2 and β = 0.75, and if the sales are 100, i.e., X = 100, the cost of goods sold would be, on average, 2 + 0.75(100) = 77. However, in any particular year when sales X = 100, the actual cost of goods sold can deviate randomly around 77. This deviation from the average is called the “disturbance” or the “error” and is represented by “e”.

Also, in the equation

Y = 2 + 0.75X + e

i.e.,

Cost of goods sold = 2 + 0.75 (sales) + e

the interpretation is that the cost of goods sold increase by 0.75 times the increase in sales. For example, if the sales increase by 20, the cost of goods sold increase, on average, by 0.75 (20) = 15. In general, we are much more interested in the value of the slope of the regression line, β, than in the value of the intercept, α.

Now, suppose we are trying to determine if there is a relationship between two variables which have apparently no relationship, say the sales of a firm, and the average height of employees of the firm. We would set up an equation like the following:

Y = α + βX + e

where

Y = sales of firm, X = average height of employees, α = intercept of the regression line, β = slope of the...

...
Unit 5 – RegressionAnalysis
Mikeja R. Cherry
American InterContinental University
Abstract
In this brief, I will demonstrate selected perceptions of the company Nordstrom, Inc., a retailer that specializes in fashion apparel with over 12 million dollars in sales last year. I will research, review, and analyze perceptions of the company, create graphs to show qualitative and quantitative analysis, and provide a summary of my findings.
Introduction
Nordstrom, Inc. is a retailer that specializes in fashion apparel for men, women and kids that was founded in 1901. The company is headquartered in Seattle, Washington with over 61,000 employees world-wide as of February 2, 2013. (Business Wire, 2014)
Nordstrom, Inc. offers on online store, e-commerce, retail stores, mobile commerce and catalogs to its consumers. It operates 117 full-line stores within the United States and 1 store in Canada, 167 Nordstrom Rack stores, 1 clearance store under the Last Chance Banner, 1 philanthropic treasure & bond store called Trunk Club and 2 Jeffrey boutiques. The option of shopping online is also available at www.nordstrom.com along with an online private sale subsidiary Hautelook. They have warehouses, also called fulfillment centers, which manages majority of their shipping needs that are located in Cedar Rapids, Iowa. (Business Source Premier, 2014)
Nordstrom, Inc. continues to make investments in their...

...the data better, you
cannot consult the regression R2 because
(a) ln(Y) may be negative for 0 < Y < 1.
(b) the TSS are not measured in the same units between the two models.
(c) the slope no longer indicates the effect of a unit change of X on Y in the log-linear
model.
(d) the regression R2 can be greater than one in the second model.
1
(v) The exponential function
(a) is the inverse of the natural logarithm function.
(b) does not play an important role in modeling nonlinear regression functions in econometrics.
(c) can be written as exp(ex ).
(d) is ex , where e is 3.1415...
(vi) The following are properties of the logarithm function with the exception of
(a) ln(1/x) = −ln(x).
(b) ln(a + x) = ln(a) + ln(x).
(c) ln(ax) = ln(a) + ln(x).
(d) ln(xa) = aln(x).
(vii) In the log-log model, the slope coefficient indicates
(a) the effect that a unit change in X has on Y.
(b) the elasticity of Y with respect to X.
(c) ∆Y/∆X.
(d)
∆Y
∆X
×
Y
X
(viii) In the model ln(Yi ) = β0 + β1 Xi + ui , the elasticity of E(Y|X) with respect to X is
(a) β1 X
(b) β1
(c)
β1 X
β0 +β1 X
(d) Cannot be calculated because the function is non-linear
(ix) Consider the following least squares specification between testscores and the studentteacher ratio:
TestScore = 557.8 + 36.42ln(Income).
According to this equation, a 1% increase income is associated with an increase in test
scores of
(a) 0.36 points
(b) 36.42 points
(c) 557.8 points
(d) cannot be...

...RegressionAnalysis Exercises
1- A farmer wanted to find the relationship between the amount of fertilizer used and the yield of corn. He selected seven acres of his land on which he used different amounts of fertilizer to grow corn. The following table gives the amount (in pounds) of fertilizer used and the yield (in bushels) of corn for each of the seven acres.
|Fertilizer Used |Yield of Corn |
|120 |138 |
|80 |112 |
|100 |129 |
|70 |96 |
|88 |119 |
|75 |104 |
|110 |134 |
a. With the amount of fertilizer used as an independent variable and yield of corn as a...

...Airlines, a commuter firm serving the Boston hub, are shown for the past 12 weeks:
|Week |1 |2 |3 |4 |5 |6 |
|Demand |17 |19 |15 |21 |20 |23 |
Problem 7 [6]
A careful analysis of the cost of operating an automobile was conducted by a firm. The following model was developed:
Y = 4,000 + 0.20X
where Y is the annual cost and X is the miles driven.
a) If the car is driven 15,000 miles this year, what is the forecasted cost of operating this automobile? [3]
b) If the car is driven 25,000 miles this year, what is the forecasted cost of operating this automobile? [3]
Problem 8[12]
A study to determine the correlation between bank deposits and consumer price indices in Birmingham, Alabama, revealed the following (which was based on n = 5 years of data):
(x = 15, (x2 = 55, (xy = 70, (y = 20 and (y2 = 130
a) What is the equation of the least square regression line? [5]
b) Find the coefficient of correlation. What does it imply to you? [4]
c) What is the standard error of the estimate? [3]
Problem 9 [8]
Given the following data, use least squares regression to develop a relation between the number of rainy summer days and the number of games lost by the Boca Raton Cardinal base ball team.
Year 1994 1995 1996 1997 1998 1999 2000...

...
Mortality Rates
RegressionAnalysis of Multiple Variables
Neil Bhatt
993569302
Sta 108 P. Burman
11 total pages
The question being posed in this experiment is to understand whether or not pollution has an impact on the mortality rate. Taking data from 60 cities (n=60) where the responsive variable Y = mortality rate per population of 100,000, whose variables include Education, Percent of the population that is nonwhite, percent of population that is deemed poor, the precipitation, the amount sulfur dioxide, and amount of nitrogen dioxide.
Data:
60 Standard Metropolitan Statistical Area (SMSA) in the United States, obtained for the years 1959-1961. [Source: GC McDonald and JS Ayers, “Some applications of the ‘Chernoff Faces’: a technique for graphically representing multivariate data”, in Graphical Representation of Multivariate Data, Academic Press, 1978.
Taking the data, we can construct a matrix plot of the data in order to take a visible look at whether a correlation seems to exist or not prior to calculations.
Data Distribution:
Scatter Plot Matrix
As one can observe there seems to be a cluster of data situated on what appears to be a correlation of relationship between Y=Mortality rate and X= potential variables influencing Y.
From this we construct a correlation matrix in order to see a relationship...

...REGRESSIONANALYSIS
Correlation only indicates the degree and direction of relationship between two variables. It does not, necessarily connote a cause-effect relationship. Even when there are grounds to believe the causal relationship exits, correlation does not tell us which variable is the cause and which, the effect. For example, the demand for a commodity and its price will generally be found to be correlated, but the question whether demand depends on price or vice-versa; will not be answered by correlation.
The dictionary meaning of the ‘regression’ is the act of the returning or going back. The term ‘regression’ was first used by Francis Galton in 1877 while studying the relationship between the heights of fathers and sons.
“Regression is the measure of the average relationship between two or more variables in terms of the original units of data.”
The line of regression is the line, which gives the best estimate to the values of one variable for any specific values of other variables.
For two variables on regressionanalysis, there are two regression lines. One line as the regression of x on y and other is for regression of y on x.
These two regression line show the average relationship between the two variables. The regression line of y on x gives the most probable...

...Introduction
This presentation on RegressionAnalysis will relate to a simple regression model. Initially, the regression model and the regression equation will be explored. As well, there will be a brief look into estimated regression equation. This case study that will be used involves a large Chinese Food restaurant chain.
Business Case
In this instance, the restaurant chain's management wants to determine the best locations in which to expand their restaurant business. So far the most successful locations have been near college campuses. This opinion is based on the positive numbers that quarterly sales (y) reflect and the size of the student population (x). Management's mindset is that over all, the restaurants that are within close proximity to college campuses with large student bodies generate more sales than restaurants located near campuses with small student bodies.
In the sample box below, xi is the size of the student population (in thousands) and yi is the quarterly sale (in thousands of dollars). The value for xi and yi for all of the 10 Chinese Food restaurants given in the sample are reflected as follows:
Sample Data:
(measured in 1,000s) (measured in $1,000s)
Restaurant Student Population Quarterly Sales
(i) (xi) (yi)
1 2 58
2 6 105
3 8 88
4 8 118
5 12 117
6 16 137
7 20 157
8 20 169
9 22 149
10 26 202
Methodology
Given the...

...RegressionAnalysis (Tom’s Used Mustangs)
Irving Campus
GM 533: Applied Managerial Statistics
04/19/2012
Memo
To:
From:
Date: April 19st, 2012
Re: Statistic Analysis on price settings
Various hypothesis tests were compared as well as several multiple regressions in order to identify the factors that would manipulate the selling price of Ford Mustangs. The data being used contains observations on 35 used Mustangs and 10 different characteristics.
The test hypothesis that price is dependent on whether the car is convertible is superior to the other hypothesis tests conducted. The analysis performed showed that the test hypothesis with the smallest P-value was favorable, convertible cars had the smallest P-value.
The data that is used in this regressionanalysis to find the proper equation model for the relationship between price, age and mileage is from the Bryant/Smith Case 7 Tom’s Used Mustangs. As described in the case, the used car sales are determined largely by Tom’s gut feeling to determine his asking prices.
The most effective hypothesis test that exhibits a relationship with the mean price is if the car is convertible. The RegressionAnalysis is conducted to see if there is any relationship between the price and mileage, color, owner and age and GT. After running several models with...

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