Reading Data

# Read data from csv into a variable called 'data'
data <- read.csv("F:/COURSERA COURSES/Regression Modeling in Practice/DataSetW.csv")

Attach the dataset

# Attach data variables
attach(data)

# Display the data summary
summary(data)
##       YEAR        ENROLL        UNEMPRATE     
##  Min.   : 1   Min.   : 5501   Min.   : 5.700  
##  1st Qu.: 8   1st Qu.:10167   1st Qu.: 7.000  
##  Median :15   Median :14395   Median : 7.500  
##  Mean   :15   Mean   :12707   Mean   : 7.717  
##  3rd Qu.:22   3rd Qu.:14969   3rd Qu.: 8.200  
##  Max.   :29   Max.   :16081   Max.   :10.100

Building Simple Linear Regression Model

# Predict the response variable Enrollments (ENROLL) using the predictor variable 
# unemployment rate (UNEMPRATE)

SLM_ENROLL <- lm(ENROLL ~ UNEMPRATE, data = data)

# Displaying The Linear Model
SLM_ENROLL
## 
## Call:
## lm(formula = ENROLL ~ UNEMPRATE, data = data)
## 
## Coefficients:
## (Intercept)    UNEMPRATE  
##        3957         1134

Summarizing the Model

# Display information about the linear model
summary(SLM_ENROLL)
## 
## Call:
## lm(formula = ENROLL ~ UNEMPRATE, data = data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -7640.0 -1046.5   602.8  1934.3  4187.2 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept)   3957.0     4000.1   0.989   0.3313  
## UNEMPRATE     1133.8      513.1   2.210   0.0358 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3049 on 27 degrees of freedom
## Multiple R-squared:  0.1531, Adjusted R-squared:  0.1218 
## F-statistic: 4.883 on 1 and 27 DF,  p-value: 0.03579

Discussion

    The results of the linear regression model indicated that Unemployement rate (Beta=1134, p=0.0358) 
    was significantly and positively associated with number of enrollments at the university.
    
    But low value of R-square also suggests that the distribution is highly scattered (high deviation) 
    around the regression line.

Sample Prediction

# what is the expected enrollment (ENROLL) for a given year's unemployment rate (UNEMPRATE)? 
# Year = 2015
# UNEMPRATE = 10%

# Then, ENROLL is:
3957 + 1134 * 10
## [1] 15297

Prediction Result Summary

The predicted enrollment at the university, for a given 10% unemployment rate, is 15,297 students in 2015.