3. Given are five observations collected in a regression study on two variables.
X1 | 2 6 9 13 20
Y1| 7 18 9 26 23
a. Develop a scatter diagram for these data.
b. Develop the estimated regression equation for these data.
c. Use the estimated regression equation to predict the value of y when x = 4.
11. Although delays at major airports are now less frequent, it helps to know which airports are likely to throw off your schedule. In addition, your plane is late arriving at a particular airport where you must make a connection, how likely is it that the departure will be late an thus increase your chances of making the connection? The following data show the percentage of late arrivals and departures during August for 13 airports.
Late Arrivals Late Departures
Airport % %
Atlanta 24 22
Charlotte 20 20
Chicago 30 29
Cincinnati 20 19
Dallas 20 22
Denver 23 23
Detroit 18 19
Houston 20 16
Minneapolis 18 18
Phoenix 21 22
Pittsburgh 25 22
Salt Lake City 18 17
St. Louis 16 16
a. Develop a scatter plot for these data with the percentage of late arrivals as the independent variable.
b. What does the scatter diagram developed in part (a) indicate about the relationship between late arrivals and late departures?
c. Use the least squares method to develop the estimated regression equation.
d. Provide an interpretation for the slope of the estimated regression equation.
e. Suppose the percentage of late arrivals at the Philadelphia airport for August was 22%. What is an estimate of the percentage of late departures?
19. Consider the following data:
Make and Model x = Reliability y = Price ($)
Acura 4 33,150
BMW 3 40,570
Lexus IS300 5 35,105
Lexus ES330 5 35,174
Mercedes 1 42,230
Lincoln 3 38,225
Audi 2 37,605
Cadillac 1 37,695
Nissan 4 34,390
Infiniti 5 33,845
Saab 3 36,910
Infiniti G35 4 34,695
Jaguar 1 37,995
Saab Arc 3 36,955
Volvo 3 33,890
The estimated regression equation for these data is y=40,639-1301.2x. What percentage of the total sum of squares can be accounted for by the estimated regression equation? Comment on the goodness of fit. What is the sample correlation coefficient?
35. Health experts recommend that runners drink 4 oz of water every 15 min. they run. All-day cross-country runs require hip-mounted or over-the-shoulder hydration systems. As the capacity for water increases, the weight and cost of these larger-capacity systems also increase. The following data show the weight (oz) and the price ($) for 26 systems.
Model Weight Price Model Weight Price
Fastdraw 3 10 Elite 14 60
Fastdraw Plus 4 12 Extender 16 65
Fitness 5 12 Stinger 16 65
Access 7 20 GelFlask 3 20
Access Plus 8 25 Geldraw 1 7
Solo 9 25 GelFlask Holster 2 10
Serenade 9 35 GelFlask SS 1 10
Solitaire 11 35 Strider 8 30
Gemini 21 45 Walkabout 14 40
Shadow 15 40 Solitude 9 35
Sipstream 18 60 Getaway 19 55
Express 9 30 Profile 14 50
Lightning 12 40 Traverse 13 60
a. Use these data to develop an estimated regression equation that could be used to predict the price of a hydration system given its weight.
b. Test the significance of the relationship at the .05 level of significance.
c. Did the estimated regression equation provide a good fit? Explain.
41. Data on x=temperature rating(Fo) and y=price($) for 11 sleeping bags provided the estimated regression equation y = 359.2668 - 5.2772x. For these data s = 37.9372.
a. Develop a point estimate of the price of a sleeping bag with a temperature rating of 30.
b. Develop a 95% confidence interval for the mean overall temperature rating for all sleeping bags with a temperature rating of 30.
c. Suppose a new model was developed with a temperature rating of 30. Develop a 95% prediction interval for the price of this new model.
d. Discuss the differences in your answers to (b) and (c).
43. Consider the following sample of production volumes and total cost data for a manufacturing operation:
Production Volume (units) Total Cost ($)
Data on the production volume x and total cost y for this manufacturing operation were used to develop the estimated regression equation y = 1246.67 + 7.6x.
a. The company's production schedule shows that 500 units must be produced next month. What is the point estimate of the total cost for next month?
b. Develop a 99% prediction interval for the total cost for next month.
c. If an accounting cost report at the end of next month shows that the actual production cost during the month was $6000, should managers be concerned about incurring such a high total cost for the month? Discuss.
The solution provides step by step method for the calculation of linear regression model. Formula for the calculation and Interpretations of the results are also included.