ETC1000 BUSINESS AND ECONOMIC STATISTICS9. Diagnostic Analytics –

Correlation

DIAGNOSTIC ANALYTICS - CORRELATION

Consider data on doctors visits:

Correlation: a measure of relationship between numerical variables.

AGE DOCVISITS EDUC MALE Income SUMMER SPRING AUTUMN WINTER48 0 14.5 1 3467.818 1 0 0 052 2 18 1 3152.017 1 0 0 049 0 12 1 1500.96 0 0 0 159 4 11.5 1 2969.174 1 0 0 039 6 10.5 1 6416.904 1 0 0 040 12 9 1 780.4994 0 1 0 058 1 16 1 2619.857 0 0 0 145 0 11.5 1 1746.571 0 0 0 128 0 11.5 1 2825.337 1 0 0 060 0 12 1 2486.298 0 1 0 051 3 11.5 1 2134.699 0 1 0 027 0 13 1 1951.249 0 1 0 024 0 10.5 1 3274.823 0 0 0 123 4 10 1 1582.19 0 1 0 033 0 18 1 1245.242 1 0 0 0

DIAGNOSTIC ANALYTICS - CORRELATION, SCATTER DIAGRAM

Scatter diagram of:education (years of education) and income (monthly $)

Suggests a modest positive relationship

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DIAGNOSTIC ANALYTICS:SCATTER DIAGRAM

Scatter diagram helps us address 3 questions:1. Is there a relationship between X & Y?

DIAGNOSTIC ANALYTICS:SCATTER DIAGRAM

2. What direction is the relationship?

DIAGNOSTIC ANALYSIS:SCATTER DIAGRAM

3. Is the relationship linear?

DIAGNOSTIC ANALYTICS:CORRELATION

Correlation measures the strength and direction of the linear relationship between X & Y.

• standard units for X & Y • product of deviations of from and from• Deviations can be positive or negative, so

their product and average can be positive or negative.

DIAGNOSTIC ANALYTICS:CORRELATION

:

X

Y

DIAGNOSTIC ANALYTICS:CORRELATION

Correlation (Education & Income) = 0.298

Correlation (Doctor’s visits & Education) = -.092 Correlation (Doctor’s visits & Income) = -.005which tells a similar story to comparing mean incomes across groups.

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