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 regression line, and e = disturbance term
Then, we would collect a sample of data from a number of firms regarding sales and average height of employees.
How to Cite this Page
MLA Citation:
"How To Analyze The Regression Analysis Output From Excel." 123HelpMe.com. 27 Jun 2017
<http://www.123HelpMe.com/view.asp?id=158859>.
Title
 Length
 Color Rating


Different Statistical Methods Essay
 ... This is the only use for a ztest (Tanner & YoussefMorgan, 2013). The one sample ttest accomplishes the same thing as the ztest. The calculated t from the sample is compared to a t value which is determined by degrees of freedom and alpha. The ttest can be onetailed or twotailed, based on what is being tested. It can be used when there are fewer than 30 items in the sample and the sample is not normally distributed. The null hypothesis is that the sample mean and population mean are statistically equal.... [tags: regression analysis, probability]
:: 4 Works Cited

798 words (2.3 pages) 
Strong Essays 
[preview] 
Regression of Baseball Player Salaries Essay
 Introduction The Major League Baseball (MLB) organization is a group of baseball teams that have made it to the Major League. The Major League Baseball data set provides the 2005 salaries of multiple Major League Baseball (MLB) teams as well as individual salaries of players within 30 teams (Lind, Marchal & Wathen, 2008). The MLB data set gives information such as batting averages, wins, salaries, home runs, errors, etc (Lind, Marchal & Wathen, 2008). Two specific teams stand out of the information when looking at their stats; St.... [tags: Statistics, Regression Paper]
:: 1 Works Cited

943 words (2.7 pages) 
Good Essays 
[preview] 
How Ethical Leadership is Associated with Employee Output and Organizational Culture
 For an effective and long term success for managers in leadership position, managers have to set an example with high moral standards and conduct that is shown in their daily activities. This kind of leadership qualities must be exerted in their everyday talk, actions, and conduct in the work environment. Today, there’s more demand to be more progressive and efficient in the work place with no room for error (Veiga, Golden, & Dechant, 2004). Also, there has been an increase in consciousness about an individual’s rights, bring in the concern about an employees’ treatment within a jobsite.... [tags: leadership, employee output, managers ethics]
:: 30 Works Cited

1944 words (5.6 pages) 
Term Papers 
[preview] 
Regression Analysis Essay
 Introduction Our regression analysis was done on OMNITRANS fuel consumption. This has been an ongoing issue for OMNITRANS where there seems to be an inconsistency with there CNG fuel consumption. There continues to be variance in what is consumed each day compared to the amount of miles driven. This issue is very important to OMNITRANS because it makes it very difficult to plan for future use with the CNG industry. OMNITRANS wants to have a consistency with CNG use so they can plan for budgeting purposes and new contracts that are connected with the CNG usage.... [tags: Statistics Regression Analysis]

1684 words (4.8 pages) 
Powerful Essays 
[preview] 
2004 MLB Wins Regression Essay
 On Wednesday, October 27th 2004, the Curse of the Bambino was finally lifted off the City of Boston and its longsuffering baseball fans (see Appendix A for more on the Curse). For the first time in 86 years, the Boston Red Sox were the world champions of baseball. There is no arguing that the 2004 Red Sox were a good team that played excellent baseball throughout the season. The team was led not by talent cultivated through the Red Sox’ farm system but by highpriced, freeagent acquisitions such as Pedro Martinez, Manny Ramirez, Keith Foulke, Curt Shilling and David Ortiz.... [tags: essays research papers]

1879 words (5.4 pages) 
Powerful Essays 
[preview] 
Essay on Regression Analysis
 Introduction Gunshot wounds; bullet caliber is increasing, a look of this increase from years 19982003. This data is derived from the use of larger caliber firearms in accidents, homicides and suicides. Data was collected from the measurements of bullets removed from trauma patients then submitted to a surgical pathology laboratory. This data was collected from the years of 1998 to 2002 with patient medical record number and the year obtained. Approximately 78 percent of all bullets were intact and sufficient for use in the study.... [tags: essays research papers]

866 words (2.5 pages) 
Strong Essays 
[preview] 
Microsoft Excel: Goal Seek and Scenarios Essay
 ... In Businesses Spreadsheets are used in different ways within business workplace. In common, spreadsheets store data, but they also provide a range of tools to manage and process the data. This makes them particularly useful for businesses environment. Through formulas, spreadsheets can perform mathematical, statistical, financial and organisational transformations and calculations. Spreadsheets also help to present data in user friendly view Businesses use spreadsheets in ways that are suited to their own services, some of the examples that business could use spreadsheets for are: Cash flow forecasting Cash flow is an accounting document used by businesses, which illustrates t... [tags: columns, rows, data]

1582 words (4.5 pages) 
Better Essays 
[preview] 
Benefits of Using Microsoft Excel Essay examples
 Benefits of Using Microsoft Excel Since the beginning of the American school system; educators have tried to improve their teaching techniques in order, to be more effective in the classroom. With the recent technological advances we have benefited from in the past couple of decades; the educational system has greatly improved. For the last ten to fifteen years, the school system has successfully phased in the curriculum frequent computer usage in the classrooms, in order to improve the students ability to adapt to the growing use of computers in the work force.... [tags: essays papers]
:: 9 Works Cited

1654 words (4.7 pages) 
Powerful Essays 
[preview] 
Management Excel Essay
 Management In Management Excel, we start with an assumption of the universality of management. Management is management. Management is generic. Management principles are general rather than specific to a type of firm or organization. However, management is universal only if the manager has become familiar with the specific situation in which it is applied. Production technology, customer characteristics and the culture of the industry are examples of specifics that managers need to learn to be effective in applying their generic management skills.... [tags: Business Management]

926 words (2.6 pages) 
Strong Essays 
[preview] 
Essay on Exploring Microsoft Excel and Microsoft Access
 Exploring Microsoft Excel and Microsoft Access Microsoft Excel is a spreadsheet application, which will enable the analysis of data because it is able to perform calculations and routine mathematical operations for example a cash flow forecast. Spreadsheet files are known as workbooks, in which you work and store your data. Because each workbook can contain many sheets, you can organise various kinds of related information in a single file. Simple formula such as using Sum will add up column or rows of data quite easily, while more complicated formulas using IF statements can compare different values and then inserts the appropriate result.... [tags: Papers]

523 words (1.5 pages) 
Good Essays 
[preview] 
Related Searches
The relationship between the two variables is estimated by a technique called the “ordinary least squares”. If indeed there is no relationship between the two variables, what do you expect the value of β, the slope of the regression line to be? We would expect this value to be zero, or some number close to it.
Though there may not be any real relationship between the two variables, the estimated value of β may not be exactly (and most probably will not be) equal to zero. But, if we were to repeat this exercise of estimating the value of β using many more samples, we would expect the value of β to be zero on average. However, we have only one sample of a certain number of firms (say, 30 firms) and we have to make an inference from this one sample whether X influences Y (i.e. β ≠ 0) or X does not influence Y (i.e. β = 0). How do we make such an inference? Testing whether β = 0 or β ≠ 0 is called the Test of Significance. In other words, we are trying to test if the independent variable X (average height in our example) is significant in explaining (or determining) what the value of Y (sales) would be. If indeed X is significant in explaining in Y, then whenever X changes we would expect Y to change in a systematic manner as well. In this case, β would not be equal to zero. However, if X is not significant in explaining Y, then changes in X would not cause systematic changes in Y. In this case, β should be STATISTICALLY close to zero.
To determine whether β is statistically close to zero (and infer whether there is any relationship at all between the variables X and Y), we can make use of various measures to make an inference regarding the significance of variable X in explaining variable Y. These measures are as follows:
R2: This statistic measures the percentage of variation in the dependent variable Y which is explained by the independent variable X. The value of R2 is always between 0 and 1. The weaker the relationship between the two variables, the closer is the value of R2 to 0. The stronger the relationship between the two variables, the closer is the value of R2 to 1.
tvalue: A rough rule of thumb to determine the significance of X in explaining Y is that the tvalue of the slope coefficient, β, should be at least 2. The greater the tvalue, the more is the evidence that X is significant in explaining Y.
Significance F: The lower this value, the stronger is the evidence that there is indeed a relationship between X and Y. If this value is less than 0.05, we would be safe in accepting that there is a relationship between X and Y.
Pvalue: Look at the pvalue of the independent variable (and not the intercept). If this pvalue is less than 0.05, we would be safe in accepting that there is a relationship between X and Y.
95% Confidence Interval: Look at the 95% confidence interval of the independent variable (not the intercept). If this confidence interval does not contain zero, we would be safe in accepting that there is a relationship between X and Y. However, if the 95% confidence interval contains zero, there is a big chance that we would making a mistake by assuming that there is a relationship between X and Y.

