October 21, 2024

Dataset freeny

data(freeny)
sprintf("No of Observation in freeny dataset : %d ",dim(freeny)[1])
[1] "No of Observation in freeny dataset : 39 "
sprintf("No of Variables in freeny dataset : %d ",dim(freeny)[2])
[1] "No of Variables in freeny dataset : 5 "
paste("Variable Names: ")
[1] "Variable Names: "
for(name in colnames(freeny)) {print(name)}
[1] "y"
[1] "lag.quarterly.revenue"
[1] "price.index"
[1] "income.level"
[1] "market.potential"

Dataset Summary freeny

head(freeny)
              y lag.quarterly.revenue price.index income.level market.potential
1962.25 8.79236               8.79636     4.70997      5.82110          12.9699
1962.5  8.79137               8.79236     4.70217      5.82558          12.9733
1962.75 8.81486               8.79137     4.68944      5.83112          12.9774
1963    8.81301               8.81486     4.68558      5.84046          12.9806
1963.25 8.90751               8.81301     4.64019      5.85036          12.9831
1963.5  8.93673               8.90751     4.62553      5.86464          12.9854
summary(freeny)
       y         lag.quarterly.revenue  price.index     income.level  
 Min.   :8.791   Min.   :8.791         Min.   :4.278   Min.   :5.821  
 1st Qu.:9.045   1st Qu.:9.020         1st Qu.:4.392   1st Qu.:5.948  
 Median :9.314   Median :9.284         Median :4.510   Median :6.061  
 Mean   :9.306   Mean   :9.281         Mean   :4.496   Mean   :6.039  
 3rd Qu.:9.591   3rd Qu.:9.561         3rd Qu.:4.605   3rd Qu.:6.139  
 Max.   :9.794   Max.   :9.775         Max.   :4.710   Max.   :6.200  
 market.potential
 Min.   :12.97   
 1st Qu.:13.01   
 Median :13.07   
 Mean   :13.07   
 3rd Qu.:13.12   
 Max.   :13.17

Dataset Pair Plots freeny

pairs(freeny, main = "Freeny Data")

Building the Regression Model: 1

Model:   \(\text{y} = \beta_0 +\beta_1\cdot\text{lag.quarterly.revenue} + \beta_2\cdot\text{price.index} + \beta_3\cdot\text{income.level} + \beta_4\cdot\text{market.potential} + \varepsilon;\hspace{1 cm}\varepsilon\sim N(0;\sigma^2)\)
Fitted: \(\text{y} = \hat{\beta_0} +\hat{\beta_1}\cdot\text{lag.quarterly.revenue} + \hat{\beta_2}\cdot\text{price.index} + \hat{\beta_3}\cdot\text{income.level} + \hat{\beta_4}\cdot\text{market.potential}\)  

Call:
lm(formula = y ~ ., data = freeny)

Residuals:
       Min         1Q     Median         3Q        Max 
-0.0259426 -0.0101033  0.0003824  0.0103236  0.0267124 

Coefficients:
                      Estimate Std. Error t value Pr(>|t|)    
(Intercept)           -10.4726     6.0217  -1.739   0.0911 .  
lag.quarterly.revenue   0.1239     0.1424   0.870   0.3904    
price.index            -0.7542     0.1607  -4.693 4.28e-05 ***
income.level            0.7675     0.1339   5.730 1.93e-06 ***
market.potential        1.3306     0.5093   2.613   0.0133 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.01473 on 34 degrees of freedom
Multiple R-squared:  0.9981,    Adjusted R-squared:  0.9978 
F-statistic:  4354 on 4 and 34 DF,  p-value: < 2.2e-16

Building the Regression Model: 2

Model:   \(\text{y} = \beta_0 +\beta_1\cdot\text{lag.quarterly.revenue} + \beta_2\cdot\text{income.level} + \beta_3\cdot\text{market.potential} + \varepsilon;\hspace{1 cm}\varepsilon\sim N(0;\sigma^2)\)
Fitted: \(\text{y} = \hat{\beta_0} +\hat{\beta_1}\cdot\text{lag.quarterly.revenue} + \hat{\beta_2}\cdot\text{income.level} + \hat{\beta_3}\cdot\text{market.potential}\)  

Call:
lm(formula = y ~ lag.quarterly.revenue + income.level + market.potential, 
    data = freeny)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.034155 -0.011470 -0.001669  0.011516  0.053271 

Coefficients:
                      Estimate Std. Error t value Pr(>|t|)   
(Intercept)           -19.9123     7.1808  -2.773  0.00884 **
lag.quarterly.revenue   0.5092     0.1472   3.460  0.00144 **
income.level            0.3808     0.1336   2.851  0.00726 **
market.potential        1.6984     0.6367   2.668  0.01149 * 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.01863 on 35 degrees of freedom
Multiple R-squared:  0.9968,    Adjusted R-squared:  0.9965 
F-statistic:  3623 on 3 and 35 DF,  p-value: < 2.2e-16

Correlation Plot : ggcorplot

M <- cor(freeny)
ggcorrplot(M, hc.order = FALSE, type = "lower",
   outline.col = "white",
   ggtheme = ggplot2::theme_gray,
   colors = c("#6D9EC1", "white", "#E46726"), lab=TRUE)

Scatter Plot between y vs lag.quarterly.revenue

Scatter Plot between y vs price.index

Scatter Plot between y vs income.level

ggplot(data = freeny, 
       aes(x=income.level,y=y))  + geom_point() + stat_smooth(method = "lm", 
        formula = y ~ x,geom = "smooth")

Scatter Plot between y vs market.potential