Correlation & Regression Part 1

Correlation analysis is to quantify the degree to which the variables are related, i.e. how well the estimating equation fits.

Regression analysis is about construction of an estimating equation that relates the predictor/s to the response.

In fact, correlation analysis is part of Regression analysis.

Typically in correlation analysis, scatterplot is a graphical analysis while we can use Pearson product moment correlation coefficient to measure the degree of linear relationship between 2 variables.

The rule of thumb is always conduct scatterplot to look for the form of relationship ( is it a line or curve? ) first. If there is linear trend, it is then necessary to proceed to Pearson correlation coefficient test to check the significance and value.

A case study below to illustrate it’s application.

A project leader wish to assess the relationship between Project Y and a parameter (X) he found which he believe it’s a significant factor. The data is as follows:

Y

7.5

7.6

8.1

8.3

8.6

9.1

9.3

9.5

9.9

10.2

10.6

10.9

11.2

11.5

11.7

X

2.2

2.4

2.6

2.8

3.1

3.4

3.7

3.9

4.1

4.4

4.7

4.9

5.1

5.4

5.6

So, the practical question here was “Was X strongly correlated with Project Y?”

In Minitab, click Graph>Scatterplot> and click OK.

image image

Select respective Y and X information below and by default, click OK.

image

The scatterplot was generated where it shown obvious form of a straight line, indicating a very strong linear trend.

image

Next, conduct Pearson correlation coefficient test with following Hypothesis Statement.

Ho : Null Hypothesis => r = 0

Ha : Alternate Hypothesis => r ≠ 0

In Minitab, click Stat>Basic Statistics>Correlation and select relevant information.

image

Click OK to find the analysis result below.

Correlations: X, Y

Pearson correlation of X and Y = 0.999

P-Value = 0.000

The Pvalue was 0.000. Reject Ho (assuming Alpha risk of 5% i.e. 0.05 )

Statistically, it was to say Pearson correlation coefficient value between Y and X  was not equal to 0.

Practically, it was concluded that there was strong linear relationship between Y and X with Pearson correlation coefficient value (r) measured as 0.999.

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About ssbblky

Six Sigma Professional
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