I developed an excel template that generates linear regression analysis. It also writes summary report which is based on correlation coefficient, p-value and beta coefficient. This spreadsheet can handle up to 10,000 cases.

In simple linear regression, we predict scores on one variable from the scores on a second variable.

The variable we predict is called the

The regression equation is written as :

Y: It is the value of the dependent variable, what is being predicted or explained

a : It is the value of Y when the value of X=0

b : How much Y changes for per unit change in X.

X: It is the value of the independent variable, what is predicting or explaining the value of Y

e: It is the error in predicting the value of Y, given the value of X

This is to test whether the regression model predicts the outcome variable significantly well.

It represents how much dependent variable changes for per unit change in independent variable.

**Download link : Linear Regression Analysis**

**Meaning :**

In simple linear regression, we predict scores on one variable from the scores on a second variable.

The variable we predict is called the

**dependent or outcome variable**and is referred to as Y. The variable we base our predictions on is called the

**independent or predictor variable**and is referred to as X.

**When there is only one independent or predictor variable, the prediction method is called simple regression.****Examples :**

- To predict employees' salary on the basis of their years of experience.
- To predict students' mathematics aptitude scores based on the number of hours they studied.

**Assumptions :**

- There must be a linear relationship between dependent and independent variable.
- Your two variables should be measured at the interval or ratio level.
- For any value of X, Y is normally distributed and the variance of Y is the same for all possible values of X.
- The Y values are statistically independent of one another.

**Regression Equation :**

The regression equation is written as :

**Y = a + bX +e**

Y: It is the value of the dependent variable, what is being predicted or explained

a : It is the value of Y when the value of X=0

b : How much Y changes for per unit change in X.

X: It is the value of the independent variable, what is predicting or explaining the value of Y

e: It is the error in predicting the value of Y, given the value of X

**Interpretation :**

Assume you want to run a regression of wage on work experience.

**Regression Equation :**

**Wage = a + b*(years of service)**

Suppose the intercept is 1.1 and slope coefficient (b) of years of service is 0.65.

An employee having 3 years of experience would be predicted to get wage of 3.05 thousand dollars.

**Wage = 1.1 + (0.65) (Years of Service)**An employee having 3 years of experience would be predicted to get wage of 3.05 thousand dollars.

**Standard Output of Linear Regression Analysis****1. R and R Square value**

**The R value indicates degree of linear relationship between two variables (Simple Correlation). The R square value indicates how much of the dependent variable can be explained by the independent variable.**

**2. Significance Testing**

This is to test whether the regression model predicts the outcome variable significantly well.

**Rule :**If p value is less than 0.05, that implies the model applied can statistically significantly predict the outcome variable.

**3. Beta Coefficient**

It represents how much dependent variable changes for per unit change in independent variable.

Good Article...

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