Question

Is there a relationship between the weight and price of a mountain​ bike? The following data set gives the weights and prices for ten mountain bikes. Let the expanatory variable x be the weight in pounds and the response variable y be the​ bike's price.
Weight​ (LB)
30
33
30
27
37
31
29
35
35
29

Price​ ($)
1100
360
560
590
140
1020
710
920
170
460
a. Construct a scatterplot. Interpret.
b. Find the regression equation. Interpret the slope in context. Does the​ y-intercept have contextual​ meaning?
c. You decide to purchase a mountain bike that weighs 3232 pounds. What is the predicted price for the​ bike?

Answer 1

Answer:

Step-by-step explanation:

Hello!

The objective is to determine if there is a linear association between the price of a mountain bike (Y) and it's the weight (X).

a.

Looking at the Scatterplot the data is dispersed in all quadrants of the graph, at first glance there seems to be some kind of functional relationship between the price and weight of mountain bike bicycles. If you are not too strict maybe there could be a slight negative relationship between them.

b.

The linear regression model is E(Yi)= α + βXi

To find the regression model for this particular set of variables you have to estimate the intercept and the slope.

a= Y[bar] - bX[bar] = 1961.40 $

b= $\frac{sum XiYi-\frac{(sumXi)(sumYi)}{n} }{sumXi^2-\frac{(sumXi)^2}{n} }$ = -42.99 $/LB

^Yi= 1961.40 - 42.99Xi

$ 1961.40 is the estimated value of the average price if the weight of the mountain bike is zero. (It has no contextual sense)

-42.99 $/LB is the modification of the estimated average price every time the weight of the mountain bike.

c.

In this item, you need yo obtain a value of price for a given value of weight. To do so all you have to do is replace the value on the estimated regression model:

^Y/X=3232= 1961.40 - 42.99*32= $585.72

I hope it helps!