Exercises. 1. The following information is obtained from a sample data set

1. The following information is obtained from a sample data set

; ; ; ;

; and

Find the values of and .

2. A sample data set produced the following information

; ; ; ;

; and

Find the values of and .

3. Computing from a data set of (x, y) values produced the following summary statistics

; ; ;

; ;

a) Obtain equation of the best fitting straight line.

b) Estimate .

4. Computing from a data set of (x, y) values produced the following

summary statistics

; ; ;

; ;

Determine the proportion of variation in y that is explained by linear regression.

5. A calculation shows that , , and , determine the proportion of variation in y that is explained by linear regression.

6. The following table lists the sizes of offices (in hundreds of square meters) and the rents (in dollars) paid for those offices.

Size of offices
Monthly rent

a) Find the regression line with the size of an office as an independent variable and monthly rent as a dependent variable.

b) Give a brief interpretation of the values of a and b.

c) Predict the monthly rent for the office with 2400 square meters.

d) One of the offices is 2600 square meters and its rent is $850. What is the predicted rent for this office? Find the error for this office.

e) Compute the standard deviation of errors.

f) Calculate the coefficient of determination. What percentage of the variation in monthly rents explained by the sizes of the offices? What percentage of this variation is not explained?

7. Refer to exercise 7 of previous chapter. The following table which gives the ages (in years) and prices (in hundred of dollars) of eight cars of specific model, is reproduced from that exercise.

Age
Price

a) Calculate the standard deviation of errors.

b) Compute the coefficient of determination and give a brief interpretation of it.

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