SIMPLE REGRESSION
Your command has asked you to investigate the relationship between the number and cost of machine breakdowns in the machine shop. The machines are old and becoming somewhat unreliable. However, the cost of replacing them is quite high, and your command is not convinced the cost of slow repair justifies purchase of new machines. To help make a decision about replacement you gathered data about last month's costs for repairs of the machines (Y) and the ages in months (X) of 20 of the command's welding machines
You have performed the following arithmetic calculations to assist you in assessing the relationship between the ages of your welding machines and the cost of repairs.
= 2,267 = 7,904.1 = 913,730.4
= 7,196.55 = 17,799.5 = 77,801.1
A. Descriptive Statistics Use your calculations above to calculate and explain the meaning of the following concepts; show your sample mean of X and Y
1.sample standard deviation of X and Y
2.coefficient of variation for X and for Y
3.sample covariance of X and Y
4.correlation of X and Y
B. Estimated Regression Model
1.Calculate the estimated regression line for this data (show your formulas).
2.Interpret the coefficients of your estimated regression model
C. Overall Goodness of Fit concepts Using your estimated regression model from above, you have calculated the Sum of Squares due to Error as 33,776.8 to assist your assessment of your model. Show your formula, calculate the value, and explain the meaning of:
Sum of Squares Total
Sum of Squares for Regression
Coefficient of Determination
What amount of the variation of cost of repairs is explained by the age of machines?
D. Significance of individual regression coefficient Using appropriate values from Parts A, B, and C, show your formula, calculate the value, and explain the meaning of the following concepts:
1.Standard error of estimate
2.t-statistic for age of machine
3.p-value for this t-statistic (Use 1-tailed hypothesis test)
4.Is there enough evidence to conclude older machines have increased monthly repair costs?
5.Is there enough evidence to conclude monthly repair costs increase by $2.25 for machines one month older?
E. Prediction Intervalsshow formula, calculations, and explain the meaning of the following:
1.A 90% confident prediction interval for cost of repair of a machine 10 years old.
2.Estimate with 90% confidence the mean cost of repair for all machines 10 years old.
MULTIPLE REGRESSION
Life insurance companies are very interested in predicting how long their customers will live. An insurance company gathered data on 100 recently deceased customers. It recorded the age at death of the customer (Y) and 4 additional variables:
MOTHER: the age at death of the customer's mother,
FATHER: the age at death of the customer's father,
GMOTHERS: the mean age at death of the customer's grandmothers, and
GFATHERS: the mean age at death of the customer's grandfathers.
What are your expected signs of the four explanatory variables and why?
Is this linear equation statistically significant? How do you know?
Write out the estimated regression model.
Interpret the coefficients of each of the explanatory variables in your estimated regression.
Which, if any, of the explanatory variables are statistically significant? How do you know?
What is the numerical value and meaning of the coefficient of determination in this estimated equation?
What variables might you want to add or drop in this model and why?