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# Statistics Exercise | Example 2 | The Answer

We solve previous statistics exercise

Solution:

1) Representation of scatter plot Mi (xi;yi) accompanied by the statistical series in an orthogonal coordinate system:

(On the abscissa axis, 2 cm represents one year, and on the ordinate axis, 1 cm represents 100 tons of fish)

2) Determining the coordinates of the centroid point G for this scatter plot.

We haveG (x̄;ȳ)where:

And from it: G(3.5;814.17).

3) Demonstrate that the least squares regression line equation is y=115x+411.67.

The equation of the regression line is of the form y=ax+b where:

and b= ȳ-ax̄  (Because G belongs to this line)

To calculate a, we use the following table:

By substituting, we find:

a=(19110 6 )(3.5×814.17)17.56

a≃ 115

And we have: bȳ-ax̄ =814.17-115(3.5)=411.67

Then: y=115x+411.67

4) Determining the production of this water reservoir in the year 2015. (All results are given rounded to 10-2).

We have: The order of the year 2015 is x=2015-2004+1=12

Then: For x=12, we find y= 115 (12) +411.67=1791.67

The production of this water reservoir in the year 2015 is 1791.67 tons.