Questions 54 through 57 refer to the following scenario.
An ecologist has tracked and studied 145 deer that were born in 1987. The number of these deer still living each year in the study were entered in the computer. Using a statistical computing package (called SPSS) the ecologist got the following regression output for regressing the number of deer still living on the number of years after 1987.
- * * * M U L T I P L E R E G R E S S I O N * * * *
Equation Number 1 Dependent Variable.. LIVING
Variable(s) Entered on Step Number 1.. YEAR
Multiple R .98343
R Square .96713
Adjusted R Square .96243
Standard Error 10.72336
Analysis of Variance
DF Sum of Squares Mean Square
Regression 1 23681.06667 23681.06667
Residual 7 804.93333 114.99048
F = 205.93937 Signif F = .0000
—————— Variables in the Equation ——————
Variable B SE B Beta T Sig T
YEAR -19.866667 1.384380 -.983426 -14.351 .0000
(Constant) 157.133333 6.590967 23.841 .0000
54.Obtain the estimated regression equation for regressing the number of deer still living on the number of years after 1987.
55.Is there evidence at the 1% level of a significant (non-zero) linear relationship between the number of years after 1987 and the number of deer still living? Explain your answer.
56.Give the estimate of the population standard deviation σ.
57.Calculate a 99% confidence interval for the true slope β1.
Questions 58 through 62 refer to the following scenario.
Current salary of men and women in managing positions depends on several factors. In a recent study, information on 84 people in managing positions was collected. Some of the variables collected were current salary, beginning salary, previous experience (in months) and length of employment (months since hire). The multiple regression model suggested is: current salary = β0 + β1(beginning salary) + β2(length of employment)
- β3(previous experience)
The data was entered into SPSS and the following output was produced.
58.Give the equation of the estimated multiple regression line for predicting current salary from beginning salary, previous experience, and length of employment.
59.What is the value of R2? What does this mean in terms of this salary problem?
60.What is the value of the estimate for the population standard deviation σ?
61.Using the p-value of the F-test in the above ANOVA table, what do you decide about the overall significance of the model?
62.Predict the current salary for a person with a management position who had a starting salary of $25,000, who has 5 years (=60 months) of experience, and who has been at this job for 6 years (=72 months).
Questions 63 through 66 refer to the following scenario.
The value of ones house depends on a multitude of components. A real estate agent collected data on 362 houses in the area where she works. Many variables are collected but she suggests using a multiple regression model that looks like:
appraised value= β0 + β1(number of rooms in the house) + β2(age of the house)
- β3(size of the lot the house sits on)
SPSS produced the following output:
63.Give the equation of the least squares regression line for predicting appraised value of the house from the number of rooms, the age of the house, and the size of the lot.
64.Predict the appraised value of a house with 6 rooms that is 15 years old and that sits on a lot of 1200 square feet (i.e. lot size = 12).
65.The value of R2 is equal to 0.229. Explain what this means in terms of the proportion of the variation in appraised value.
66.Examine the T-tests given in the output. For each of the 4 t-values, state the hypotheses being tested, the corresponding p-value, and your decision at the 1% significance level.
67.Recent studies have indicated a correlation between chess playing and grades among inner city children. Some news reports have suggested that chess playing CAUSES the improvement of children’s intelligence and grades. Explain why we cannot conclude causality from a correlation. Provide at least one alternative explanation for this correlation.