Answer to Question #289540 in Macroeconomics for Prince Anarfo

Question

Consider the following data

 

Y

X

5

64

2

87

12

50

9

71

15

44

6

56

25

42

16

60

Plot a graph of Y against X

Find the correlation between Y and X

Test at 5% level of significance whether the correlation is significant or not

Answer 1

let's solve it in EXCEL

The correlation coefficient (r) is -0.768.

The relationship between the studied signs is inverse, the closeness (strength) of the connection on the Cheddock scale is high.

The number of degrees of freedom (f) is 6.

the Student's t-criterion is 2.937.

The critical value of the Student's t-test for a given number of degrees of freedom is 2.447.

t observations > t critical, the dependence of features is statistically significant (p=0.032380).

Equation of paired linear regression: y = 76.66037 - 1.54759x.

The coefficient of determination r2 is 0.590 (the factorial feature x determines 59% of the variance of the dependent feature y).

The average approximation error (characterizes the adequacy of the regression model) is 14.5%.