Reading 11, Putting the puzzle of Reading 11 together

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. Hypothesis testing & confidence intervals

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