Business Statistics :regression equation

Problem #5 Outside Magazine
Outside Magazine tested 10 different models of day hikers and backpacking boots. The following data show the upper support and price for each model tested. Upper support was measured using a rating from 1 to 5, with a rating of 1 denoting average upper support and rating of 5 denoting excellent upper support (Outside Magazine Buyer's Guide, 2001).
Manufacturer and Model Upper Support Price ($)
Salmon Super Raid 2 120
Merrell Chameleon Prime 3 125
Teva Challenger 3 130
Vasque Fusion GTX 3 135
Boreal Maigmo 3 150
L.L. Bean GTX Super Guide 5 189
Lowa Kibo 5 190
Asolo AFX 520 GTX 4 195
Raichle Mt. Trail GTX 4 200
Scarpa Delta SL M3 5 220
a. Use these data to develop an estimated regression equation to estimate the price of a day hiker and backpacking boot given the upper support rating.
b. At the .05 level of significance, determine whether upper support and price are related.
c. Would you feel comfortable using the estimated regression equation developed in part (a) to estimate the price for a day hiker or backpacking boot given the upper support rating?
d. Estimate the price for a day hiker with an upper support rating of 4.

Problem #6 Trial Runner Gear Guide
Health experts recommend that runners drink 4 ounces of water every 15 minutes they run. Although handled bottles work well for many types of runs, all-day cross-country runs require hip-mounted or over-the-shoulder hydration systems. In addition to carrying more water, hip-mounted or over-the-shoulder hydration systems offer more storage space for food and extra clothing. As the capacity increases, however, the weight and cost of these larger-capacity systems also increase. The following data show the weight (ounces) and the price for 26 hip-mounted or over-the-shoulder hydration systems (Trial Runner Gear Guide 2003).

Model Weight (oz.) Price ($)
Fastdraw 3 10
Fastdraw Plus 4 12
Fitness 5 12
Access 7 20
Access Plus 8 25
Solo 9 25
Serenade 9 35
Solitaire 11 35
Gemini 21 45
Shadow 15 40
SipStream 18 60
Express 9 30
Lightning 12 40
Elite 14 60
Extender 16 65
Stinger 16 65
GelFlask Belt 3 20
DelDraw 1 7
GelFlask Clip-on Holster 2 10
GelFlask Holster SS 1 10
Strider (W) 8 30
Walkabout (W) 14 40
Solitude I.C.E. 9 35
Getaway I.C.E. 19 55
Profile I.C.E. 14 50
Traverse I.C.E. 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 0.05 level of significance.
c. Did the estimated regression equation provide a good fit? Explain.
d. Assume that the estimated regression equation developed in part (a) will also apply to hydration systems produced by other companies. Develop a 95% confidence interval estimate of the price for all hydration systems that weigh 10 ounces.
e. Assume that the estimated regression equation developed in part (a) will also apply to hydration systems produced by other companies. Develop a 95% prediction interval estimate of the price for the Back Draft system produced by Eastern Mountain Sports. The Back Draft System weighs 10 ounces.

See attached file for full problem description.