+65-85483705
Select Page

# R-squared in Simple Linear Regression Analysis

## 1. R-squared in Regression Analysis

The r-squared is also called coefficient of determination. It shows the proportion of the total variation of the dependent variable can be explained by independent variables. However, this value can be inflated as the number of independent variables increases. Thus, some people prefer to use the adjusted r-squared. This concept is likely to be introduce during the university statistics lessons.

## 2. Formula for calculating R-squared

R-squared = Sum of square of residual / Sum of square of total

Exercise

Calcuate the R-squared for the following regression lines.

Question 1

 Y1 X1 10 12 15 15 13 10 14 15 10 15 14 15 13 15 13 11 10 10 10 15 10 10 14 11 10 14 11 11 10 11 13 15 14 12 10 14 10 11 13 10 10 10

Question 2

 Y2 X2 10 14 11 13 12 15 15 14 13 15 12 15 13 11 10 10 15 10 12 15 11 12 15 10 12 15 13 15 15 14 14 14 13 10 12 10 15 13 10 15 11 12

Question 3

 Y3 X3 10 14 10 13 12 13 10 11 14 13 13 12 14 14 15 12 13 13 12 10 12 10 12 14 15 15 10 15 14 11 14 13 15 14 12 10 10 11 10 15 14 10

Question 4

 Y4 X4 11 11 14 12 14 10 12 14 14 10 12 10 12 11 13 12 10 15 11 10 14 15 12 11 12 13 11 11 11 14 12 12 14 13 12 13 14 15 12 13 10 15

Question 5

 Y5 X5 12 12 10 12 11 10 15 14 10 10 11 14 10 11 12 10 10 15 12 14 14 14 10 14 11 15 13 15 14 14 13 15 10 13 14 11 13 13 15 11 15 10

Question 6

 Y6 X6 11 11 14 12 14 13 14 10 10 12 15 12 13 15 15 10 12 12 12 10 15 11 10 10 12 10 15 10 12 10 14 13 14 10 12 11 11 12 11 12 12 11

1. 0.059
2. 0.014
3. 0.000
4. 0.015
5. 0.000
6. 0.000

## About the Math Tutor - Dr Loo

I am a PhD holder with 9 years of teaching experience at secondary school and university. My expertizes are mathematics, statistics, econometrics, finance and machine learning.

Currently I do provide consultation and private tuition in Singapore. For those who are looking for math tutor in Singapore or statistics tutor in Singapore, please feel free to contact me at +65-85483705 (SMS/Whatsapp/Telegram).

Some of the math tuition in Singapore I provide includes O-level math tuition and also JC Math Tuition (H1 Math Tuition & H2 Math Tuition). On the other hand, my statistics tuition in Singapore mostly focus on pre-university level until postgraduate level. For those who prefer online tutoring service, the online O-level math tuition and online JC math tuition are also available.

## For those who are looking for math tution in Singapore

Need help with this topic? I do provide mathematics home tuition in Singapore for O-level math and also JC H2 math. In addition, online math tutoring is available as well. Feel free to contact me if you would like to know further.