Level 2, Volume 1, Quantitative methods, Reading 11, Correlation & Regression
Most questions related to Reading 11 incorporate tables as indicated below.
I struggled initially to understand the relevance and links between the data. After I studied it in some detail I came to the conclusion that if you understand the table, you understand most of Reading 11.
These tables are a bit like a big puzzle, and once you start to piece it together Reading 11 falls into place. This is pretty cool.
Below I use the information from Reading 11, Table 12 and show all the links and relationships using underlying formulas.
Did I say it is pretty cool?
Information from Reading 11, Table 12
Regression Statistics | |
Multiple R | 0.928 |
R-Squared | 0.861 |
Observations | 60 |
Standard error of estimate | 0.0174 |
ANOVA | Degrees of Freedom | Sum of Squares | Mean Sum of Squares | F |
Regression | 1 | 0.1093 | 0.1093 | 359.64 |
Residual | 58 | 0.0176 | 0.0003 | |
Total | 59 | 0.1269 |
Coefficients | Standard Error | t-Statistic | |
Alpha | 0.0009 | 0.0023 | 0.4036 |
Beta | 0.7902 | 0.0417 | 18.9655 |
1.Calculate Correlation Coefficient (“CC”)using Coefficient of Determination (“CD”)
Remember R-Squared = Coefficient of Determination
1.1 Reference
Reading 11, 3.4
1.2.1 Formula: Method 1
CD = Square the CC between the dependent and independent variables.
Thus CC = √CD
1.3.1 Using information from the tables:
CC = √0.861 = 0.928
We can therefore also conclude that Multiple R = Correlation Coefficient
1.2.2 Formula: Method 2
Sum of Squares are used to calculate variation. Residual variation is the same as unexplained variation.
= 1 - (Unexplained variation/Total Variation)
1.3.2 Using information from the tables:
= 1 – (0.0176/0.1269)
= 0.928
2. Calculate Standard Error of Estimate
2.1 Reference
Reading 11, 3.3
2.2 Formula
2.3 Using information from the tables:
We know that Residual Sum of Squares is the same as Sum of Error Squares.
Therefore:
√(0.0176/(60-2))
= √0.0003
= 0.0174
3. Calculating Means (Residual)
(0.0176/(60-2))
=0.0003
4. Calculate ANOVA using the F test
4.1 Reference:
Reading 11, 3.6
4.2 The formula:
4.3 Using information from the tables:
(0.1093/1) / (0.0176/(60-2))
= 360.193
(Difference due to rounding. As indicated in text book)
5. Link between F test & t-statistic
5.1 Reference
Reading 11, 3.6
5.2 Formula
For one independent variable the F-statistic is the square of the t-statistic for the slope coefficient.
5.3 Using information from the tables:
t- statistic = √F statistic
= √359.64
= 18.9655
6. Calculating the t-statistic
6.1 Reference
Reading 11, 2.6
6.2 Formula
6.3 Using information from the tables:
0.928. √(60-2) / √(1-0.928²)
18.9655 |
7.1 Reference
Reading 11, 3.5
7.2 Formula
This formula equals 0
7.3 Using information from the tables:
0 = 0.7902 +/- (x)(0.0417)
+/- X = 18.94
