Notes in Regression1, Lecture notes of Mathematics

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Regression

Analysis

STATISTICS AND PROBABILITY

How to Interpret Coefficient in Regression Analysis

Interpreting Regression Coefficients for Linear Relationships

>The sign of a regression coefficient tells you whether there is a positive or

negative correlation between each independent variable the dependent variable.

>A positive coefficient indicates that as the value of the independent variable

increases, the mean of the dependent variable also tends to increase.

>A negative coefficient suggests that as the independent variable increases, the

dependent variable tends to decrease.

Interpreting Regression Coefficients for Linear Relationships

The coefficient value signifies how much the mean of the

dependent variable changes given a one-unit shift in the

independent variable while holding other variables in the

model constant.

This property of holding the other variables constant is

crucial because it allows you to assess the effect of each

variable in isolation from the others.

1. What is the independent variable?
2. What is the dependent variable?
3. What should be in the vertical axis?
4. What should be in the horizontal axis?
5. What is the regression equation?
6. What is the height coefficient?
7. This coefficient represents the mean increase of ______ in (unit) for every additional one (unit) in ________.
8. If your _______ increases by 1 (unit) the average ______ increases by 106.5 (unit).

The height coefficient in the regression equation is 106.5. This coefficient represents the mean increase of weight in kilograms for every additional one meter in height. If your height increases by 1 meter, the average weight increases by 106.5 kilograms.

P-values and coefficients in regression analysis work together to tell you which relationships in your model are statistically significant and the nature of those relationships.

The coefficients describe the mathematical relationship between each independent variable and the dependent variable. The p-values for the coefficients indicate whether these relationships are statistically significant.

Interpreting P-Values for Variables in a Regression Model

> Regression analysis is a form of inferential statistics.

>The p-values help determine whether the relationships that you observe in your

sample also exist in the larger population.

>The p-value for each independent variable tests the null hypothesis that the

variable has no correlation with the dependent variable.

> If there is no correlation, there is no association between the changes in the

independent variable and the shifts in the dependent variable. In other words,

there is insufficient evidence to conclude that there is effect at the population level.

Ho : r = 0

H 1 : r ≠ 0

p value > significance level

On the other hand, a p-value that is greater than the

significance level indicates that there is insufficient

evidence in your sample to conclude that a non-zero

correlation exists.

Example 2 The regression output example above shows that the South and North predictor variables are statistically significant because their p-values equal 0.000. On the other hand, East is not statistically significant because its p-value (0.092) is greater than the usual significance level of 0.05. It is standard practice to use the coefficient p-values to decide whether to include variables in the final model. For the results above, we would consider removing East. Keeping variables that are not statistically significant can reduce the model’s precision.