Question

 

The dataset RacingBicycles.xlsx lists the weight (in pounds) and price for a sample of racing bicycles with weight as a predictor of price. Using the approximation method discussed in class and represented by the formulas below,

Construct and interpret a 93% confidence interval for the mean price of racing bicycles that weigh 15.5 pounds.

Construct and interpret a 93% prediction interval for the price of a racing bicycle weighing 15.5 pounds.

Brand	Weight	Price
FELT F5	17.8	2100
PINARELLO Paris	16.1	6250
ORBEA Orca GDR	14.9	8370
EDDY MERCKX EMX-7	15.9	6200
BH RC1 Ultegra	17.2	4000
BH Ultralight 386	13.1	8600
CERVELO S5 Team	16.2	6000
GIANT TCR Advanced 2	17.1	2580
WILIER TRIESTINA Gran Turismo	17.6	3400
SPECIALIZED S-Works Amira SL4	14.1	8000

Answer 1

Lease square regression equation.

Y = b₀ + b₁ *x

Or Price= b₀ + b₁ * Weight

b₀ is Intercept , we can find intercept using excel function =INTERCEPT( Y data set column range, x data set column range )

b₁ is Slope , we can find slope using excel function =SLOPE( Y data set column range, x data set column range )

So b₀ = 28574.1 and b1 = -1439.01

regression equation : Price= 28574.1 - 1439.01 * Weight

We are given weight = 15.5

Therefore predicted price = 28574.1 - (1439.01 * 15.5 )  

Predicted price ( ) = 6269.503

a) Confidence interval =  

We are given confidence level = 93% , therefore α = 1- 0.93 = 0.07 and df = 10 - 2 = 8  

We can find using excel function =TINV( 0.07 ,8 ) = 2.09

We can find Se using excel function =STEYX( y data set ,x data set) = 942.2661

We can find using excel function =AVERAGE(x data set ) = 16

SS_xx = = 21.74

Confidence interval =  

We are 93% Confidence that the mean price of racing bicycles that weigh 15.5 pounds is between ( 5611.911 , 6927.095 )

b) Prediction interval =

=

We are 93% Confidence that the mean price of racing bicycles that weigh 15.5 pounds is between ( 4193.278 , 8345.729 )