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

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simplelucker's profile pic

simplelucker | (Level 1) eNoter

Posted on

Here, the linear regression of dependent variable (population, Y) versus independent variable (number of years elapsed since 1948, X) can be calculated as follows:

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

After performing the regression analysis (refer to the attached image), we get:

b=12636423.46 a=393329.71

So, the equation for the best fit line is Y=393329.71+12636423.46X

R=0.94

For the years 1980 (X=33), and 1995 (X=48), values of the dependent variable (population) are:25616304 and 31516250 respectively.

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mathewww | High School Teacher | (Level 1) Honors

Posted on

In an alternative method, the approximated data in the excel-generated equations are calibrated around the midpoint of the spreadsheet (i.e. the year 1960) and used in the given situation.

From the R^2 values, it is quite evident that both the equations are equally good.

The calculations are done on the basis of the simpler, linear equation.

The linear equation, as generated in the excel spreadsheet is: Y=393330*X-8E+08

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

Y=393330*X-7.53017800E+08

Substituting X for the years 1980 and 1995, we get the values of the dependent variable (population) as: 25775600 and 31675550 respectively.

mathewww's profile pic

mathewww | High School Teacher | (Level 1) Honors

Posted on

Here, the linear regression of dependent variable (population, Y) versus independent variable (number of years elapsed since 1948, X) can be calculated as follows:

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

After performing the regression analysis (refer to the attached image), we get:

b=12636423.46 a=393329.71

So, the equation for the best fit line is Y=393329.71+12636423.46X

R=0.94

For the years 1980 (X=33), and 1995 (X=48), values of the dependent variable (population) are: 25616304 and 31516250 respectively.

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