At the end of each calendar year, employees of the G. G. Green Manufacturing Com
ID: 3298484 • Letter: A
Question
At the end of each calendar year, employees of the G. G. Green Manufacturing Company can purchase company stock. For a sample of employees, the Director of Human Resources investigated the relationship between the number of years of service with the company and the number of shares of company stock owned. The “number of years of service” is used to estimate the “number of shares of stock”. Use the following output showing the results of the analysis to answer the questions.
questions.
ANOVA Table
Source
SS
df
MS
F
Regression
152,399.0211
1
152,399.0211
62.67
Residual
55,934.1189
23
2,432.9182
Total
208,333.1400
24
Regression Output
Variables
Coefficients
Std. Error
T (df = 23)
Intercept
197.9229
34.3047
5.770
Years
24.9145
3.1473
7.916
How many employees were included in the study?
Is “number of shares of stock” or “number of years of service” the dependent variable?
Write out the regression equation.
Is the relationship between the two variables direct or indirect?
Determine the correlation coefficient.
How many shares would you expect an employee of 10 years to own?
For each additional years of service, how much does “number of shares owned” change?
Can we conclude that as years of service increases, so do the number of shares of stock owned? Conduct an appropriate test of hypothesis on the slope of the regression line.
Source
SS
df
MS
F
Regression
152,399.0211
1
152,399.0211
62.67
Residual
55,934.1189
23
2,432.9182
Total
208,333.1400
24
Explanation / Answer
All answers answered in detail . Please give us a positive feedback in case I've managed to help you with my answers.
How many employees were included in the study?
We get this from total df in the table.
total df = n-1 , so n = df+1 = 24+1 = 25
Is “number of shares of stock” or “number of years of service” the dependent variable?
Look at the Regression output table. Years is one of predictor variables
Therefore, Years is independent variable, Number of shares of stock is dependent variable.
Write out the regression equation.
Nos. shares = 197.9229 + 24.9145*Years
Is the relationship between the two variables direct or indirect?
It is direct since the variable Years is been used directly to predict the number of shares.
Determine the correlation coefficient.
correlation coefficient is the square root of Rsquare
Rsquare is ration of variance explained out of total variance.
Therefore, Rsqaure = 152.399/208.333
Hence, correlation coeff= sqrt(152.399/208.333) = .8553
r = .8553
How many shares would you expect an employee of 10 years to own?
Just sub Years = 10, in the regresison equation, Nos. shares = 197.9229 + 24.9145*10 = 447 shares
So, if you had worked for 10 years, you would have gotten 447 shares
For each additional years of service, how much does “number of shares owned” change?
For each additional years of service you would have got 24.9145 or roughly 25 shares. This we get from the coefficient of Years.
In statistic' terms, it can be interpreted as "how much will Dependent variable change for a unit increase in Independent variable"
Can we conclude that as years of service increases, so do the number of shares of stock owned? Conduct an appropriate test of hypothesis on the slope of the regression line.
So, t = ( 24.9145 - 0)/(3.1473) = 7.916 at a df =23, which is definitely above the critical t value of +/- 2.06865761
So, hypothesis of slope reveals that variable "Years" is significant
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