Question

 

A story in the Wall Street Journal reveals that “Tall Workers Earn More Money”. Ron, the president of a company, wants to know whether the relationship between salary and height exists in his own company, and obtains the following data from the human resources department.

a. Calculate the correlation between salary and height, and describe the relationship between these two variables.

b. How much of the variability in salary can be accounted for by height?

c. Is there a significant correlation between salary and height?

Employee	Salary (X) (in $1000s of dollars)	Height (Y) (in inches)
Max	45	72
Jacob	38	70
Jesse	39	74
Jennifer	33	60
Jeremy	40	63
Brian	36	68
Barbara	42	67
Benny	35	64
Rhonda	47	77
Kelly	45	69
Miriam	37	67
Gloria	34	66
Shirley	42	70
Eden	46	73

Answer 1

a) type all data in Excel and

Data -> data analysis-> correlation -> choose both x and y simulatenously. -> ok

We get correlation coefficient as r= 0.7247

Here the correlation is positive and we can see a correlation between salary and height even though it is not strong( because it is not close to one) , fairly a correlation.

Height and salary are correlated that means there exist a good linear relationship between them.

b)Data- data analysis- regression - choose x and y values -ok

We get the regression equation as

x= -10.6223+ .7372y ( because x is dependent variable and y is independent)

And coefficient of determination= R2= .5252

Ie almost 52.52% of variability in salary can be explained by the height variable. [ Because coefficient of correlation accounts for the percentage that the change in or variation in dependent variable is explained by the independent variable] so here almost 60 % variation in salary is explained by the independent variable height .

c) to test the significance of correlation ,

Test H0: rho =0

H1 : rho not equal to zero

Where rho is the population correlation.

Test Statistic is t= r√(n-2) / √(1-r2)

Which follows t with n-2 degrees of freedom.

On substituting values t = 3.6434

t value corresponding to n-2 degrees of freedom = +_ 2.179

P value = 0.003367

So at 5% level we reject null hypothesis. Since p value is less than alpha =0.05

ie rho not equal to zero, means there is a significant correlation.