use the most accurate equation to predict the dependent variable for the years 1980 and 1995.

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mathewww | High School Teacher | (Level 1) Honors

Posted on

Alternatively, the approximated data in the excel-generated equations should be calibrated around the midpoint of the spreadsheet in order to fit in the given situation.

From the R^2 values, it is quite evident that the polynomial equation is the most accurate equation that fits the given situation.

The best fit equation, as generated in the excel spreadsheet is: Y=13.509*X^2-51309*X+5E+07

Calibrating it around the year 1960 (i.e. the midpoint) gives the exact best fit equation as:

Y=13.509*X^2-51309*X+4.8809159E+07

For the years 1980 and 1995, the number of deaths can be obtained by substituting the years for X in the final equation.

The corresponding values of the dependent variable are 178023 and 213862 respectively.

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mathewww | High School Teacher | (Level 1) Honors

Posted on

A linear regression predicts the values of a dependent variable (number of deaths, Y) based upon the values of an independent variable (number of years elapsed, X). Correlation analysis is used to measure the strength of association between the two variables X and Y.

Beginning with the start of year 1948, the number of years elapsed is the independent variable (x) and the number of deaths is the dependent variable (y) here.

Let the equation for the best fit line is Y=a+bX

The steps of regression analysis are as follows:

Year    X           Y           X^2         Y^2                    XY

---------------------------------------------------------------------

1948     1       122974       1       15122604676       122974

1949       2         124567       4     15516937489       249134

1950    3        124220       9        15430608400        372660

-------   ---         -------------   --   -----------------   --------------

-------   ---         -------------   --   -----------------   -------------

1971    24         157272   576       24734481984        3774528

1972    25       162413   625       26377982569       4060325

-------------------------------------------------------------------------------

 SUM    325         3498743     5525     4.93247E+11         47622261

     (`barX` =13, `barY` =139949.72)

    ` b=(sum(XY)-(sumXsumY)/n)/(sumX^2-(sumX)^2/n)`

         =(47622261-325*3498743/25)/(5525-325^2/25)

         =1645.08

a=`barY` -b*`barX` =139949.72-1645.08*13

=118563.7

`R=(sum(XY))/(sqrt(sumX^2sumY^2))`

=47622261/sqrt(5525*4.93247E+11)

=0.912245

Therefore, the equation of the best fit line is Y=575737.4-33522.13X

For the year 1980 (X=33), and 1995 (X=48), values of the dependent variable (number of deaths) are: 172851 and 197527 respectively.

%MCEPASTEBIN%

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