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Regression : key information

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1. List one unclear concept regarding regression and provide an example from your personal or work life where regression could be used to show a relationship between two variables.

2. Correlation does not equal causation. That is very important to understand when interpreting regression. Can anyone elaborate for me?(100+ words please)

(ii) One should never use a regression line to predict the dependent response variable when the independent value is outside of the data range of the original data set that was used to fit the line. Explain why.(100+ words Please)

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Question No.1
List one unclear concept regarding regression and provide an example from your personal or work life where regression could be used to show a relationship between two variables.

Solution:
Regression analysis will show us how to determine both the nature and the strength of a relationship between variables.
I have considered my own data to show a relationship between two variables.
Assessed Price (000) Size (Sq. Ft)
1796 4790
1544 4720
2094 5940
1968 5720
1567 3660
1878 5000
949 2990
910 2610
1774 5650
1187 3570
1113 2930
671 1280
1678 4880
710 1620
678 1820

By using least square method, the estimated regression line is y = 173.46 + 0.313 X

On substituting different values of X we can estimate the Y-value. When we substitute higher values ...

Solution Summary

The solution discusses the key concepts in regression analysis. Examples from the experts personal and work life are examined.

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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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