Question

7. (16 pts, varied) Refer to the following data and scatterplots to respond to questions 7a-f. 25 Individual Age Score on Earning Potential 20 1 5 19 2. 15 24 56 78 76 3 8 Score on Earning Potential 10 4 8 5 7 5 6 80 35 32 14 7 12 10 20 0 30 60 70 40 50 Age 8 42 18 9 2 18 17 Figure A 10 1 11 20 35 36 25 12 16 13 29 10 20 14 19 60 65 15 15 13 Score on Earning potential 16 78 11 10 5 0 0 10 20 30 40 Age Figure B do Page 4 of 6

Answer 1

Given :- We have the given dataset consist of "age" and "score of earning potential".And the scatter plot between these two variables.

Where,Figure A is scatter plot

Fiigure B is Regression line on this plot

Figure C is ellipse drawn around the data points.

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We have to answer the questions below with the help of given scatter plot.

Below is the Scatter Plot using Excel:-

ScoreOfEarningPotential 25 20 15 Score 10 5 0 0 20 40 60 80 100 Age

1) What is the overall direction of the direction of the correlation?

Answer:- Overall direction of the correlation in the problem is positive. But it is not at all true for all observations we can say this in context of maximum observation.

2) Estimate the strength of the correlation between these variables.

Answer:- The correlation between these two variables is given by the below formula

$Cor(Age,Score)=Cov(Age,Score) / \sigma _{age} *\sigma _{score}$

We will calculate it using excel as "=correl(array1,array2)"

Hence

Cor(Age, Score) = 0.177867

This is the strength of the correlation between age and score

3) What is the direction and strength of the correlation when age is more than 60?

Answer:- The direction of this correlation is "negative" i.e from 60 as age increase score of earning potential decreases.

The strength is calculated as the correlation between age and score, when age >60

correl= - 0.92248

4) Explantion for (3) why is it so?

Answer:- It is showing the significance to the real life scenarios of human life. We know that an ordinary human can work with its whole energy till the age 55 to 60 but after that he can work efficiently as his/her body is getting older.

Due to this kind of the scenario we are observing such direction and strength.

5) It is always benificial to observe such data into the different parts.Because as explained in the part(4) the data may have two types correlation exists in it. So it is advisable to to study such into two or more parts.

6) The relationship identified here is not that much strong in the first part(positive side) but it is more stronger in the second part(negative).This statement is based on the correlaton that we have calculated in the above statement.