Exercises. 1. Plot the following straight lines

1. Plot the following straight lines. Give the values of the y- intercept and slope for each of these lines and interpret them. Indicate whether each of the lines gives a positive or negative relationships between x and y.

a) ; b)

2. The following information is obtained from a sample data

; ; ; ;

Find the estimated regression line.

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

; ; ; ;

;

Obtain the equation of the estimated regression line.

4. Given the five pairs of values,

x	0 1 6 3 5
y	4 3 0 2 1

a) Construct a scatter diagram

b) Calculate the least squares estimates a and b.

c) Determine the fitted line and draw the line on the scatter diagram.

5. A researcher took a sample of 36 electronic companies and found the following relationship between x and y where x is the amount of money (in thousands of dollars) spent on advertising by a company during a year and y represents the total gross sales (in thousands of dollars) of that company in that year.

a) An electronic company spent 2000$ on advertising during a year. What are its expected gross sales for that year?

b) Suppose five electronic companies spent 2000$ each on advertising during that year. Do you expect these five companies to have the same actual gross sales for that year? Explain.

6. An economist wanted to determine whether or not the amount of phone bills and income of households are related. The following table gives information on the monthly incomes (in hundreds of dollars) and monthly telephone bills (in dollars) for a random sample of 10 households

Income
Phone bill

a) Find the regression line with income as an independent variable and the amount of the phone bill as a dependent variable.

b) Give an interpretation of the values of a and b calculated in part a.

c) Estimate the amount of the monthly phone bill for a household with a monthly income of $2500.

7. An auto manufacturing company wanted to investigate how the price of one of its car models depreciates with age. The research department at the company took a sample of 9 cars of this model and collected the following information on the ages (in years) and prices (in hundreds of dollars) of these cars.

Age
Price

a) Construct a scatter diagram for these data. Interpret your results.

b) Find the regression line with price as a dependent variable and age as an independent variable.

c) Give a brief interpretation of the values of a and b calculated in part b.

d) Predict the price of a 4 year-old car of this model.

e) Estimate the price of a 19-year-old car of this model. Comment on this finding.

8. Construct a scatter diagram for the data in the following table

x	0.5 1 1.5
y	2 1 3

a) Plot the following two lines on your scatter diagram

1) and 2)

b) Which of these lines would you choose to characterize the relationship between x and y?Explain

c) Show that the sum of errors for both of these lines equals 0.

d) Which of these lines has smaller SSE?

e) Find the least squares regression line for the data and compare it to two lines described in part a.

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