Exercise 9 A
Exercise 9
1. A farmer wanted to find the relationship between the amount of fertilizer used and the yield of corn. He selected seven acres of his land on which he used different amounts of fertilizer to grow corn. The following table gives the amount of fertilizer (in pounds) used and the yield of corn (in bushels)for each of the seven acres.
Fertilizer Used (x)
120
80
100
70
88
75
110
Yield of Corn(y)
138
112
129
96
119
104
134
a. Find the least squares regression line.
a. Calculate r and r2 and explain what they mean.
b. Predict the yield of corn if the fertilizer used is 105 pounds.
c. Construct a 98% confidence interval for B.
d. Test at the 5% significance level if B is different from zero.
2. The following table gives information on the lowest ticket price (in dollars) and the average attendance (rounded to the nearest thousand) for the past year for sixfootball teams.
Ticket Price (x)
12.5
9.5
10
14.5
16
12
Attendance (y)
56
65
71
69
55
42
a. Find the least squares regression line.
b. Interpret the meaning of the values of a and b calculated in part (a).
c. Construct a 90% confidence interval for B.
d. Test at the 2.5% significance level if B is negative.
3. It is believed that the annual repair cost (in RM) for a car, y , is related to its age (in years), x. The simple linear regression and correlation analysis is performed to a sample of 10 cars. The simple linear regression line is = 65.0467+11.3216 x and the linear correlation coefficient is r = 0.8674.
a. What is the repair cost of a 6.25 year-old car?
b. Given. Find the value of .
c. Find the value of.
d. Construct a 99% confidence interval for B.
e. Testing at 1% significance level, can you conclude that B is different from 0?
1. A farmer wanted to find the relationship between the amount of fertilizer used and the yield of corn. He selected seven acres of his land on which he used different amounts of fertilizer to grow corn. The following table gives the amount of fertilizer (in pounds) used and the yield of corn (in bushels)for each of the seven acres.
Fertilizer Used (x)
120
80
100
70
88
75
110
Yield of Corn(y)
138
112
129
96
119
104
134
a. Find the least squares regression line.
a. Calculate r and r2 and explain what they mean.
b. Predict the yield of corn if the fertilizer used is 105 pounds.
c. Construct a 98% confidence interval for B.
d. Test at the 5% significance level if B is different from zero.
2. The following table gives information on the lowest ticket price (in dollars) and the average attendance (rounded to the nearest thousand) for the past year for sixfootball teams.
Ticket Price (x)
12.5
9.5
10
14.5
16
12
Attendance (y)
56
65
71
69
55
42
a. Find the least squares regression line.
b. Interpret the meaning of the values of a and b calculated in part (a).
c. Construct a 90% confidence interval for B.
d. Test at the 2.5% significance level if B is negative.
3. It is believed that the annual repair cost (in RM) for a car, y , is related to its age (in years), x. The simple linear regression and correlation analysis is performed to a sample of 10 cars. The simple linear regression line is = 65.0467+11.3216 x and the linear correlation coefficient is r = 0.8674.
a. What is the repair cost of a 6.25 year-old car?
b. Given. Find the value of .
c. Find the value of.
d. Construct a 99% confidence interval for B.
e. Testing at 1% significance level, can you conclude that B is different from 0?