The data below shows the relationship between the number of years that employees
ID: 3132273 • Letter: T
Question
The data below shows the relationship between the number of years that employees have worked in the foreign office of an international company and their annual income in thousands. Find the equation of the regression line for the given data. What would be the best predicted income for an individual who has been employed by the company for 8 years? Round the regression line values and mean to the nearest hundredth, and round the predicted score The decision to use y hat or the mean of y was based upon what computed value? Is this prediction reasonable given this data set?Explanation / Answer
x = number of years employed.
y = annual income.
Regression equation we can find by using MINITAB.
steps :
Enter all the data in MINITAB sheet --> Stat --> Regression --> Regression --> Response : y --> Predictors : x --> Results : select second option --> ok --> ok
Output is :
The regression equation is
y = 53.6 + 4.96 x
Given that x=8 years then,
y = 53.6 + 4.96*8
y = 93.28
The decision to use y^ or ybar was based upon testing correlation coefficient.
The test of hypothesis is,
H0 : rho = 0 Vs H1 : rho not=0
where, rho is population correlation coefficient.
Assume alpha = 0.05
The test statistic is,
t = r*sqrt(n-2) / sqrt(1-r2)
r is the sample correlation coefficient.
n is the nymber of data pairs.
r we can find by using R-sq.
r = sqrt(R-sq)
r = sqrt(0.62) = 0.7874
t = 0.7874*sqrt(9-2) / sqrt(1 - 0.78742) = 3.3795
P-value we can find by using EXCEL.
syntax is,
=TDIST(x, deg_freedom, tails)
where x is test statistic value.
deg_freedom = n-1 = 9 - 1 = 8
tails = 2
P-value = 0.01
P-value < alpha
Reject H0 at 5% level of significance.
Conclusion : Population correlation coefficient is differ than 0.
Therefore we use y^.
when x = 8 years then y^ = 93.28 and it is reasonable given this data set.
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