Statistics : Linear Regression made easy !!

A Simple Linear Regression is a straight line relationship between dependent and independent variable.




The above diagram describes, fitting a straight line to describe the relation between two variables. The points on the graph are randomly chosen observations of the two variables. The straight line describes the general movement of the data - an increase in Y(dependent) corresponding to an increase in X(independent). An inverse straight line relationship is also possible.

Simple Linear Regression Model:

Model must contain two parameters i.e. population intercept and population slope.

The method that will give us good estimates of the regression coefficients is the method of least squares.

We should come up with a line that is best fit with the data points and minimizes the errors i.e. we should minimize the sum of squared errors (SSE as in ANOVA)

Below are few formulas for calculating SSE, bo and b1.

Note:

Y is the dependent  and X is the independent variable

Example:

A study was conducted to determine the relation between travel(X) and charges(Y) on American Express card as they believe that their cardholders use their card most extensively than other cards.

Below is the data:

• X and Y are Miles and Dollars respectively. 
• X square , Y square and XY for easy calculation. 

Let us see the manual calculation for building the linear regression model i.e. Y=bo + b1X

Our model is Y=274.85 + 1.26X

Let us check the same in tools like SAS and R

SAS

Below is the code and the output which gives the same result as manual calculation

Code:

FILENAME REFFILE '/home/test/linear_reg_data.xlsx';

PROC IMPORT DATAFILE=REFFILE

DBMS=XLSX

OUT=WORK.IMPORT;

GETNAMES=YES;

RUN;

proc reg data=import;

model dollars=miles;

run;

Output:

R Studio

Code

library(readxl)

linear_reg_data <- read_excel("C:/Users/pc/Desktop/linear_reg_data.xlsx")

View(linear_reg_data)

plot(dollars~miles, data=linear_reg_data)

model1=lm(dollars~miles,data=linear_reg_data)

summary(model1)

Output:

Call:

lm(formula = dollars ~ miles, data = linear_reg_data)

Residuals:

    Min      1Q      Median      3Q     Max 

-588.79 -263.96   63.52     200.68  498.66 

Coefficients:

                    Estimate     Std. Error    t value    Pr(>|t|)    

(Intercept) 274.84969    170.33684   1.614      0.12    

miles         1.25533        0.04972       25.248   <2e-16 ***

---

Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 318.2 on 23 degrees of freedom

Multiple R-squared:  0.9652, Adjusted R-squared:  0.9637 

F-statistic: 637.5 on 1 and 23 DF,  p-value: < 2.2e-16

The model is same in all the tools and manual calculation 😊😊

SAS Example : Daily Sales Report Automation

The purpose of this post is to give an idea on automation of report generation. 

The below code generates Automated Sales Summary Email based on discrete sales figures on a product, place, cost & revenue by utilizing macros.

Create a sample sales data as below:

data sales;
input product_id place $ product_cost product_revenue ;
date=today()-1;format date date9.;
cards;
101 goa 100 200
101 punjab 100 250
101 mumbai 100 300
101 chennai 100 175
101 kerala 100 225
102 goa 200 400
102 punjab 200 450
102 mumbai 200 400
102 chennai 200 475
102 kerala 200 425
;
run;

SAS dataset:

Macro to generate sales report daily:

The SAS macro generates the sales stats and sends an email automatically without manual intervention.


%macro sales_report();

/* macro variable to capture yesterday's date*/
%let date=%sysfunc(putn(%eval(%sysfunc(today())-1),date9.));
%put &date.;

/* filter yesterday's sales data*/
data sales_fltr;
set sales;
where date="&date."d;
run;

/* Mention email id to which the report has to be generated. Modify the subject if required */

   filename temp email to="your_email@gmail.com"
            subject="Sales report - &date. "
            type="text/html";

   ods html body=temp;

   proc sql;
   select product_id,
    sum(product_cost) as total_cost,
    sum(product_revenue) as total_revenue,
    calculated total_revenue-calculated total_cost as profit
   from sales_fltr
   group by product_id;
   run;

   ods html close;

%mend;
%sales_report;

Email:

SAS output: