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Regression..stuck :(

Hey,

Im really stuck on the first part of this question. I attempted a,c,d but i don't think they're right. Could someone please give me guidance.
And how do i go about attempting question b?

Traffic planners investigated the relationship between traffic density (number of cars per mile) and the average speed of the traffic on a moderately larger city throughfare. The data were collected at the same location at 10 different times over a span of 3 months. They found a mean traffic denstiy of 68.6 carsper mile (cpm) with standard deviation 27.07 cpm. Overall, the cars' average speed was 26.38mph, with standard deviation 9.68 mph. These researchers found the regression line for there data to be:

Speed = 50.55-0.352Density


a) Use the formula b1=r(sy/sx) to work out the value of the correlation coeficcient between speed and density.)

b1= r (sy/sx)

0.352 = r (27.07/50.55)

0.352 = r 0.54

0.352/0.54 = r

0.65

After looking back at this, it doesn't appear to be right

b) What percent of the variation in average speed is explained by traffic density?

c) Predict the average speed of traffic on the throughfare when the traffic density is 50cpm.

50.55 - 0.352 (50) = 32.95

Average speed = 33mph

d) What is the value of the residual for a traffic density of 56cpm with an observed speed of 32.5mph?

50.55-0.352(56)=30.838

32.5 - 30.838=1.662

Value of her residual = 1.662


Thanks for your time
xx
Reply 1
Avatar for vc94
vc94
12
For a) y=speed, x=density. Also b1= -0.352. Should get r= -0.984

For part b) you get this by calculating (r^2)x100.

Rest looks fine.
Reply 2
Avatar for stem01
stem01
OP
thanks for your help.

So,

b1= r (sy/sx)

-0.352 = r (9.68/27.07)

-0.352 = r 0.35759

-0.352/0.35759 = r

-0.984 = r?


Regarding question b, i just do:

(-0.984^2)x100

= -96.8256

= -97%

Do you have to include the minus or does it not matter?


Thanks so much for your help
xx
Reply 3
Avatar for vc94
vc94
12
stem01
thanks for your help.

So,

b1= r (sy/sx)

-0.352 = r (9.68/27.07)

-0.352 = r 0.35759

-0.352/0.35759 = r

-0.984 = r?


Regarding question b, i just do:

(-0.984^2)x100

= -96.8256

= -97%

Do you have to include the minus or does it not matter?


Thanks so much for your help
xx


When you square a negative it becomes positive: 96.8%

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