Model Weight (lb) Price $

Fierro 7B 17.9 2200

HX 5000 16.2 6350

Durbin Ultralight 15 8470

Schmidt 16 6300

Wsilton Advanced 17.3 4100

bycyclette velo 13.2 8700

Supremo Team 16.3 6100

XTC Racer 17.2 2680

D’Onofrio Pro 17.7 3500

America #6 14.2 8100

a) There is a negative correlation between the weight (lb) and the price in dollars ($).

The curve is negative sloping meaning that an increase in weight lead to an increase in price in dollars.

SUMMARY OUTPUT

Regression Statistics

Multiple R 0.929366408

R Square 0.86372192

Adjusted R Square 0.84668716

Standard Error 942.2660545

Observations 10

ANOVA

df SS MS F Significance F

Regression 1 45017877.46 45017877.46 50.70349813 9.99374E-05

Residual 8 7102922.539 887865.3174

Total 9 52120800

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%

Intercept 28818.00368 3267.256839 8.820244351 2.14888E-05 21283.6959 36352.31146 21283.6959 36352.31146

X Variable 1 -1439.00644 202.0895123 -7.120638885 9.99374E-05 -1905.025691 -972.9871886 -1905.025691 -972.9871886

b) Estimated regression Equation

Y=-1439.01x+28818

c)Test whether each of the regression parameters , and is equal to zero at 0.05 level of significance

t-Test: Two-Sample Assuming Unequal Variances

Weight (lb) Price $

Mean 16.1 5650

Variance 2.415555556 5791200

Observations 10 10

Hypothesized Mean Difference 0

df 9

t Stat -7.403289999

P(T<=t) one-tail 2.04457E-05

t Critical one-tail 1.833112933

P(T<=t) two-tail 4.08913E-05

t Critical two-tail 2.262157163

The criteria is to reject the hypothesis when t statitic is greater than t critical two tail

In this case, we fail to reject the hypothesis since the t stat is less than t critical two tail.

d) How much variation in the prices of bicycles in the sample

R squared 0.86372192

e)The manufacturers of the D’Onofrio Pro plan to introduce the 15-lb D’Onofrio Elite bicycle later this year

Regression

Y=-1439.01x+28818

Y=-1439.01*15+28818

$50,403.15

f)She will not make room in her inventory for the bicycle unless its estimated price is less than $7,000.

Regression

28818-1439.01*15

7232.85

Since the estimated price for D'Onofrio Elite bicycle is approximately $7233 which is greater than $ 7000, the owner should not make room for this bicycle.

a) Scatter chart

Line speed (ft min) No of Defective parts Found

20 21

20 19

40 15

30 16

60 14

40 17

b) Regression Equation

Y=0.1478X+22.174

c) Test whether each of the regression parameters is equal to zero at a 0.01 significance level

t-Test: Two-Sample Assuming Unequal Variances

Variable 1 Variable 2

Mean 35 17

Variance 230 6.8

Observations 6 6

Hypothesized Mean Difference 0

df 5

t Stat 2.86521543

P(T<=t) one-tail 0.017595503

t Critical one-tail 3.364929999

P(T<=t) two-tail 0.035191007

t Critical two-tail 4.032142984

The criteria is to reject the hypothesis when t statitic is greater than t critical two tail

The analysis shows that t stat is 0.035 which is less than t critical for two tail. Therefore, we reject the hypothesis.

d) R squared

SUMMARY OUTPUT

Regression Statistics

Multiple R 0.859726954

R Square 0.739130435

Adjusted R Square 0.673913043

Standard Error 1.489090764

Observations 6

ANOVA

df SS MS F Significance F

Regression 1 25.13043478 25.13043478 11.33333333 0.028134748

Residual 4 8.869565217 2.217391304

Total 5 34

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%

Intercept 22.17391304 1.652745896 13.41640786 0.000178521 17.58515479 26.7626713 17.58515479 26.7626713

Line speed (ft min) -0.147826087 0.043910891 -3.366501646 0.028134748 -0.269742265 -0.025909908 -0.269742265 -0.025909908

d) the variation 0.739130435