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
