Question

5. Technological advances helped make inflatable paddlecraft suitable for backcountry use These blow-up rubber boats, which can be rolled into a bundle not much bigger than a golf bag, are large enough to accommodate one or two paddlers and their camping gear. Canoe & Kayak magazine tested boats from nine manufacturers to determine how they would perform on a three-day wilderness paddling trip. One of the criteria in their evaluation was the baggage capacity of the boat, evaluated using a 4-point rating scale from 1 (lowest rating) to 4 (highest rating). The following data show the baggage capacity rating and the price of the boat (Canoe & Kayak, March 2003) Baggage Capacity Price (S) Boat 4 S14 1595 Orinoco 4 1399 Outside Pro 4 1890 795 600 Explorer 380X 3 2.5 River XK2 Sea Tiger Maverik II 4 1995 1205 Starlite 100 Fat Pack Cat 2 583 1048 a. Develop a scatter diagram for these data with baggage capacity rating as the independent variable b. What does the scatter diagram developed in part (a) indicate about the relationship between baggage capacity and price? c. Draw a straight line through the data to approximate a linear relationship between baggage capacity and price d. Use the least squares method to develop the estimated regression equation e. Provide an interpretation for the slope of the estimated regression equation f. Predict the price for a boat with a baggage capacity rating of 3

Answer 1

a.

The scatter diagram for the given data is,

4.0 3.5 3.0 2.5 2.0 Baggage Capacity Price ($) 1800 2000 1200 1400 1600 000 009 008

b.

We see that the Price increases with increase in Baggage Capacity. So there is a strong positive relationship between baggage capacity and price.

c.

4.0 3.5 3.0 2.5 2.0 Baggage Capacity Price ($) 1800 2000 1200 1400 1600 000 009 008

d.

From the data,

29.5

y11110

101.25

ry= 39326

ΣΤΕΙΣΣ α)"/n-101.25-29.5?/9-4.555556 τρ

y)/n 39326 (29.5 11110)/9 2909.889 Sry xy-(

x/n 29.5/9 3.277778

y y/n 11110/9 1234.444

Slope = Sxy / Sxx = 2909.889 / 4.555556 = 638.7561

Intercept = $\bar{y}$ - slope * $\bar{x}$ = 1234.444 - 638.7561 * 3.277778 = -859.2567

The least squares regression line is,

y = -859.2567 + 638.7561 x

e.

The Price will increase by $638.7561 for each unit increase in baggage capacity.

f.

For baggage capacity of 3, the predicted price is,

y = -859.2567 + 638.7561 * 3

= $1057.012