Please provide answers in Minitab when possible.

Exercise 1

The data file Income contains the annual disposable income and total annual consumption for 12 families selected at random from a metropolitan area. It is desired to use the income to predict the annual consumption. (file: Income)

1. Find the least squares regression equation.
2. What percentage of the variation in y is being explained by the linear relationship?
3. Construct a 90% confidence interval for the slope.
4. Is this linear relationship significant? State the hypotheses tested, the p-value and the conclusion.
5. Give an estimate of .
6. What is the value of the correlation coefficient? Can we say that the greater income a family has, it causes the family to consume more?

Exercise 2

An appraiser of real estate must use data such as square footage of a house, as well as location, depreciation, and physical condition of the neighborhood to derive the appraisal value of a house. An equation might be helpful in determining appraisal values. Use the data file Real Estate to answer the following. The file contains the variables VALUE, SIZE (in square feet), CONDITION (a physical condition index), and DEPRECIATION (a depreciation factor). (file: Real Estate)

1. Is the model with all three independent variables significant? Explain.
2. Give an interpretation of the coefficient for the variable depreciation.
3. Predict the value of a house with 1800 square feet, a condition index of .1 and a depreciation factor of 0.6.
4. Give a 95% confidence interval for the average value of a house with the characteristics listed in part c.
5. Analyze the residuals for this model. Does this model fulfill the assumptions for a multiple regression model? Explain.
6. Compare the 3 variable model to a model with only the size of the house. Test to determine which model is better to use.

Exercise 3

A study of employee productivity is conducted with employees who enter data at computers. The amount of data entered is the dependent variable. Two factors that may influence productivity are the type of keyboard used (KEYBOARD) of which there are three types and time of day (TIME). For the TIME variable, 1=morning and 2=afternoon. (file: Productivity)

1. Do the factors type of keyboard and time of day and their interaction appear to influence productivity? Explain your answer by stating any hypotheses tested, the p-value and your conclusions.
2. Which level of the variable keyboard gives the greatest productivity? Explain.
3. Using the model with time and keyboard, but no interaction, form 95% Tukey intervals for the levels of keyboard type. Are any significantly different? If so which ones?
4. Repeat the analysis in part c, but remove the time factor from the analysis. Is there a difference in the results? Why?

12.64

Material and labor costs. Many companies must accurately estimate their costs before a job is begun in order to acquire a contract and make a profit. For example, a heating and plumbing contractor may base cost estimates for new homes on the total area of the house and whether central air conditioning is to be installed.

1. Write a main effects model relating the mean cost of material and labor, E(y) , to the area and central air conditioning variables.
2. Write a complete second-order model for the mean cost as a function of the same two variables.
3. What hypothesis would you test to determine whether the second-order terms are useful for predicting mean cost?
4. Refer to part c. The contractor samples 25 recent jobs and fits both the complete second-order model (part b) and the reduced main effects model (part a), so that a test can be conducted to determine whether the additional complexity of the second-order model is necessary. The resulting SSE and R ² values are shown in the table. Is there sufficient evidence to conclude that the second-order terms are important for predicting the mean cost? Use \(\alpha =.05\).

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