How Adjusted R-squared value is different from multiple R-squared value

linear_regression
r

#1

I am currently solving one regression problem using linear regression in R. I have created a linear regression model after creating the model I have used the summary function on to it. I find two terms Multiple R-squared and Adjusted R-squared.

 model1=lm(Price ~ HarvestRain+WinterRain,data=wine)
 summary(model1)

Call:
lm(formula = Price ~ HarvestRain + WinterRain, data = wine)

Residuals:
    Min      1Q  Median      3Q     Max 
-1.0933 -0.3222 -0.1012  0.3871  1.1877 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  7.865e+00  6.616e-01  11.888 4.76e-11 ***
HarvestRain -4.971e-03  1.601e-03  -3.105  0.00516 ** 
WinterRain  -9.848e-05  9.007e-04  -0.109  0.91392    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.5611 on 22 degrees of freedom
Multiple R-squared:  0.3177,    Adjusted R-squared:  0.2557 
F-statistic: 5.122 on 2 and 22 DF,  p-value: 0.01492

I want to know how this two are different from each other and which one of them better tells about the significance of the variable. So that I can select the variable for model accuracy.


#2

@hinduja1234 -
Multiple R-squared - Compares the best model to a baseline model.

Adjusted R-squared - Compares the explanatory power of regression model that contains a different number of predictors.

Adjusted R-squared tells better about if we should add a new variable or not because If you keep adding variables (predictors) to your model, R-squared will improve - that is, the predictors will appear to explain the variance - but some of that improvement may be due to chance alone. So adjusted R-squared tries to correct for this, by taking into account the ratio (N-1)/(N-k-1) where N = number of observations and k = number of variables (predictors).

Hope this helps!

Regards,
Harry