Question

MAT 152 Lab 4   

Show your work, where appropriate. Remember that you do not have to show any work for what you enter into your graphing calculator.

CITY is the city fuel consumption in miles per gallon and HWY is the highway fuel consumption in miles per gallon.

Car			City (x)		Hwy (y)
	Acura RL	18		26
	Audi A6	21		29
	Buick LaCrosse	20		30
	Chrysler 300	17		25
	Infiniti M35	18		25
	Mazda 3	26		32
	Mercury Gr Marq	17		25
	Nissan Altima	23		29
	Pontiac G6	22		32
	Toyota Avalon	22		31

For parts A – C, find each of them. (There is no work required since your graphing calculator gives you these values.)                  Round each number to 3 decimal places.  

1. the linear regression equation:

2.    the correlation coefficient, r:

3. the coefficient of determination, r2:

4. Interpret r by explaining this value (from #2 above) in a COMPLETE sentence.
   

There is a _______________ _______________ linear correlation between city and

Choose strong or weak.    Choose positive or negative.

highway fuel consumption.

5. Interpret r2 by explaining this value (from #3 above) in a COMPLETE sentence by filling in the blanks:

_________ % of the variation in _______________ mileage can be explained by the

                Change r2 to a %.                                  Choose city or highway.

                regression equation.

            _________% of the variation is unexplained.

6. Determine if there is a significant linear relationship between city and highway fuel consumption at α=0.05 by completing the hypothesis test steps below.                                                                                                                                                 (Use LinRegTTest.)   

1. H₀:

H_a:

2. Calculate the test statistic: t = ___________                  Round to 3 decimal places.

3. Calculate the p-value: ____________                              Round to 4 decimal places.

4. Select the correct decision: Reject H₀                 or         Fail to Reject H₀

5. Conclusion: (Explain in terms of if there is a significant linear relationship or not).

Answer 1

Sl.NO	City(x)	Hwy(y)	x^2	y^2	xy
1	18	26	324	676	468
2	21	29	441	841	609
3	20	30	400	900	600
4	17	25	289	625	425
5	18	25	324	625	450
6	26	32	676	1024	832
7	17	25	289	625	425
8	23	29	529	841	667
9	22	32	484	1024	704
10	22	31	484	961	682
Total	204	284	4240	8142	5862
Average	20.4	28.4

Sxx	78.4
Syy	76.4
Sxy	68.4

let the   linear regression equation be y = a + bx

b = Sxy/Sxx = 68.4/78.4 = 0.872

a = 28.4 - 0.872*20.4 = 10.602

linear regression equation y = 10.602 + 0.872x

b)  the correlation coefficient, r = Sxy/sqrt(Sxx*Syy) = 68.4/sqrt(78.4*76.4) = 0.884

There is a strong positive linear correlation between city and highway fuel consumption.

c) coefficient of determination, r2 = (correlation coefficient)2 = 0.8842 = 0.781

78.1 % of the variation in highway mileage can be explained by the regression equation.

21.9% of the variation is unexplained.

Determine if there is a significant linear relationship between city and highway fuel consumption at α=0.05 by completing the hypothesis test steps below

H0: b = 0 (slope coefficient is zero)

Ha: b 0 (slope coefficient is significantly different from zero)

Test statistic t = slope coefficient/standard error

standard error = = = 0.163

t = 0.872/0.163 = 5.350

p-value = 0.0007

Since p-value < alpha Reject H0

Hence there is a sufficient evidence to conclude that there exist a significant linear relationship between ity and highway fuel consumption.