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    QTDM Unit-2 Correlation & Regression Analysis

    Uploaded by

    Aishwarya Manish

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    © All Rights Reserved
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    QTDM Unit-2 Correlation & Regression Analysis

    Uploaded by

    Aishwarya Manish
    47 views12 pages

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    QTDM Unit-2 Correlation & Regression Analysis

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    Download as pptx, pdf, or txt
    47 views12 pages

    QTDM Unit-2 Correlation & Regression Analysis

    Uploaded by

    Aishwarya Manish

    Copyright:

    © All Rights Reserved
    Download as PPTX, PDF, TXT or read online from Scribd
    Download as pptx, pdf, or txt
    of 12

    Correlation & Regression

    Analysis
    Correlation Analysis
    • The analysis of ‘Association’ or ‘Relationship’
    between two variables.
    • Study of how Y would behave when X changes
    • Will Y increase or decrease or remain
    unchanged when X increases?
    • Correlation is not Causation
    • Scatter diagram is used to graphically
    represent Correlation.
    Coefficient of Correlation (r)
    • Karl Pearson’s Correlation Coefficient (r)
    • r can take a value only between -1 to +1.
    • r > 0 indicates positive correlation between X
    and Y
    • r < 0 indicates negative correlation between X
    and Y
    • r = 0 indicates No correlation between X and Y
    Coefficient of Correlation (r)
    • r value indicates direction and strength of
    Correlation.
    • 0 < r < 0.5 indicates a Weak Positive
    Correlation
    • 0.5 < r < 1 indicates a Strong Positive
    Correlation
    • r = 1 indicates a Perfect Positive Correlation
    Coefficient of Correlation (r)
    • r = 0 indicates No correlation
    • -0.5 < r < 0 indicates A Weak negative
    correlation
    • -1 < r < -0.5 indicates A Strong negative
    correlation
    • r = -1 indicates A Perfect Negative Correlation
    Example-1
    The following data gives information on GDP
    growth rate (X) (%) and Sales growth rate in
    automobiles (Y) (%)
    X 5.6 6.7 6.2 5.8 6.0 7.0 6.5 7.2
    Y 6.8 7.8 7.5 7.0 6.8 7.9 7.3 7.6

    Draw scatter diagram, calculate r and interpret.


    Example-2
    The following data pertains to Sales calls made
    by Sales Team and Customer Orders received
    Sales Calls 62 82 57 102 113 127 98 130
    Customer 8 9 8 9 6 9 8 10
    Orders

    Draw scatter diagram, calculate r and interpret.


    Example-3
    The Plant Manager of a manufacturing firm wants to
    understand the relationship between Training and
    Defective %.
    X: Average Training hours (per employee per year)
    Y: Defective %
    X 16.5 17.8 15.2 14.0 21.7 20.5 20.3 18.7
    Y 3.8 3.4 4.0 4.5 2.4 2.8 3.0 3.6

    Draw scatter diagram, calculate r and interpret.


    Regression Analysis
    • Relationship in an equation form between a
    Dependent variable and an Independent
    variable.
    • Simple linear regression
    • Used to estimate / predict the value of
    Dependent variable when value of
    Independent variable is known.
    • Used as a Forecasting tool.
    Example-4
    X 102.5 100 98.7 104.5 106 101.8 98.2 109 111

    Y 32 34 41.2 38 34.5 37.4 35 34.5 39.6

    Draw scatter diagram, calculate r and interpret.


    Also find the regression line equation,
    coefficient of regression, coefficient of
    determination & interpret.
    Estimate Y for X = 107
    Example-5
    X 15 18 19 17 12 21 24 25 27

    Y 3.7 3.9 4.2 3.8 2.9 5.0 5.3 5.5 5.5

    Draw scatter diagram, calculate r and interpret.


    Also find the regression line equation,
    coefficient of regression, coefficient of
    determination & interpret.
    Estimate Y for X = 30
    Example-6
    X 7.8 9.0 8.5 7.5 8.3 10.1 9.7 7.2 8.4 9.0 9.3

    Y 5.9 4.7 5.0 6.5 5.4 4.1 4.4 6.7 5.5 4.2 4.0

    X : Cost on preventive healthcare (% of GDP per annum)


    Y: No. of patient admissions in public hospitals (mn)
    Draw scatter diagram, calculate r and interpret.
    Also find the regression line equation, coefficient of
    regression, coefficient of determination & interpret.
    Estimate No. of patient admissions if 12.5% of GDP is
    spent on preventive healthcare.

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