Statistics Exercise | Example 1 | The Answer

 

We solve previous statistics exercises

Solution:

1. Representing the table with a scatterplot Mi(xi;yi) in a perpendicular coordinate system with origin o' (30;11) and a scale of 1 cm for every 5 years on the axis of abscissa and 2 cm on the axis of ordinates.

2. a) Assigning the coordinates of point G as the center of the scatterplot.

We have point G (x̄;ȳ), where:

  

And from it: G(50;13)

b) Representation of point G in the previous chart. (represented in the diagram above)

3. Finding the equation of the least squares regression line: y=ax+b, a and b are given rounded to 10^-2.

The regression line equation has 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=(45937)−(50×13)7007=(45937)−(650)100

                                                        a ≃0.06

And we have: b= ȳ-ax̄ =13-0.06(50)=10

Then: y=0.06x+10

4) Plot this line in the previous coordinate system. (represented in the diagram above)

5) We have: The man is 70 years old then:  x=70

When substituting in the equation of a straight line, we find:

y=0.06 (70)+10=14.2

Since 14.2 ≠ 15.2 Therefore, this is unreasonable according to this modification.

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