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Theory, analysis and interpretation of regression

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Theory of regression:
How does regression relate to linear algebra?

Regression terms and symbols:
What is the difference between strong negative and strong positive?

Practical examples of regression analysis:
When would you use regression correlation at a place of employment, or in education, or in politics?

Interpretation of regression outputs in Microsoft Excel:
How do you identify outliers in your data? How do they impact your regression equation?

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https://brainmass.com/statistics/linear-regression/theory-analysis-and-interpretation-of-regression-82314

Solution Preview

Linear Algebra describes a very powerful method of solving linear equations by matrix method. Since in regression we need to solve for the coefficients of the regression line, matrix method can be used to this end. In this way, linear algebra can help perform linear regression.

The correlation coefficient is a number between -1 and 1 which measures the degree to which two variables are linearly related. If there is perfect ...

Solution Summary

This solution explains regression in terms of linear algebra, strong negative and positive, practical examples, and outliers.

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Regression Analysis

a. How do I convert the above information to an equation I can use? Write out that equation using the numbers provided and the following information:
Sales (S) is the dependent variable
Advertising Expense (A) is the independent variable
b. Someone who knows statistics told me that the t value (labeled t stat in boldface above) refers to the significance of the X variable. They used a table to tell me the t value of 8.4 indicates that the X variable is statistically significant at the .05 level. What does that mean in practical terms?
c. What would this firm's sales be if it didn't advertise? How does one interpret that number, that is, what does it represent?
d. There is something basically wrong with the regression equation (the answer to part a), i.e. the equation describes a relationship that probably isn't correct. Explain what is wrong and why?

Suppose your employer buys you a copy of Excel and you decide to learn regression analysis. You gather some historical data on Sales and Advertising expenses and run a simple regression using Sales as the dependent variable and Advertising Expense as the independent variable. The results you get are shown below, with the relevant items I want you to focus on in boldface. After pondering the results a while, you show the data to your boss and she asks the questions listed below the table. Answer the questions, keeping in mind that you are explaining your answers to a supervisor who is not conversant with economic theory. Note: the key to this question is that you are being asked to provide statistical answers, but phrasing the explanations for the statistics in a fashion that a non-statistical person can understand (a very real and common situation).

Regression Statistics
Multiple R 0.834
R Square 0.747
Adjusted R Square 0.75
Standard Error 317.105
Significance F .00001

Coefficients Standard Error t Stat P-value Lower 95%
Intercept 10,000.0 81.72330008 0.551528 0.588449 -127.3486476
X Variable 1 -5.5 0.153318278 8.4 9.61E-06 0.627810145

a. How do I convert the above information to an equation I can use? Write out that equation using the numbers provided and the following information:
Sales (S) is the dependent variable
Advertising Expense (A) is the independent variable
b. Someone who knows statistics told me that the t value (labeled t stat in boldface above) refers to the significance of the X variable. They used a table to tell me the t value of 8.4 indicates that the X variable is statistically significant at the .05 level. What does that mean in practical terms?
c. What would this firm's sales be if it didn't advertise? How does one interpret that number, that is, what does it represent?
d. There is something basically wrong with the regression equation (the answer to part a), i.e. the equation describes a relationship that probably isn't correct. Explain what is wrong and why?

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