Correlation & Regression Part 2

In previous blog, it was shown how to make use of scatterplot to detect linear trend and correlation analysis to quantify Pearson correlation coefficient value.

The Pearson correlation coefficient value was determined as 0.999 ( positive correlated ) and it was very strong linear relationship between the Y and X. ( Note that Pearson correlation value lie in the range -1 ≤ r ≤ +1 )

It can then be proceeded Regression analysis for constructing an estimating equation that relates Y and X.

In Minitab, click Stat>Regression>Fitted Line Plot. Fill up relevant Y and X field below and by default, click OK.

image image

The Fitted Line Plot was generated and results interpreted below.

image

The analysis result from Session window interpreted as follows:

Regression Analysis: Y versus X

 

The regression equation is

Y = 4.739 + 1.251 X

 

 

S = 0.0776200   R-Sq = 99.7%   R-Sq(adj) = 99.7%

 

 

Analysis of Variance

 

Source      DF       SS       MS        F      P

Regression   1  27.3417  27.3417  4538.14  0.000

Error       13   0.0783   0.0060

Total       14  27.4200

 

The Null Hypothesis and Alternate Hypothesis are identified below.

Ho : Null Hypothesis => The prediction equation is not statistically significant – no relationship exists between X and Y

Ha : Alternate Hypothesis => The prediction equation is statistically significant – a relationship does exists between X and Y

Since Pvalue = 0.000, reject Ho and accept Ha.

Hence, the estimating equation is a significant model that can be used for prediction.

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About ssbblky

Six Sigma Professional
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