Question

Suppose you are interested in buying a new Toyota Corolla. You are standing on the sales lot looking at a model with different options. The list price is on the vehicle. As a salesperson approaches, you wonder what the dealer invoice price is for this model with its options. The following data are based on a random selection of Toyota Corollas of different models and options. Let y be the dealer invoice (in thousands of dollars) for the given vehicle.

x	12.8	12.9	12.8	13.6	13.4	14.2
y	11.4	11.7	11.5	12.2	12.0	12.8

Verify that Σx = 79.7, Σy = 71.6, Σx² = 1060.25, Σy² = 855.78, Σxy = 952.53, and r ≈ 0.991.

Verify that S_e ≈ 0.0791, a ≈ -0.291, and b ≈ 0.920

Answer for 1% level of significance to test the claim that ρ > 0 is

t	14.57
critical t	3.75

Find a 95% confidence interval for y when x = 13.4 (thousand dollars). (Use 2 decimal places.)

lower limit
upper limit

Answer for a 1% level of significance to test the claim that β > 0 is

t	14.57
critical t	3.75

Find a 95% confidence interval for β and interpret its meaning. (Use 2 decimal places.)

lower limit
upper limit

Answer 1

using excel>data>data analysis>Regression

we have

Simple Linear Regression Analysis
Regression Statistics
Multiple R	0.9907
R Square	0.9815
Adjusted R Square	0.9769
Standard Error	0.0791
Observations	6
ANOVA
	df	SS	MS	F	Significance F
Regression	1	1.3283	1.3283	212.2117	0.0001
Residual	4	0.0250	0.0063
Total	5	1.3533
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-0.2913	0.8398	-0.3469	0.7462	-2.6229	2.0404
x	0.9203	0.0632	14.5675	0.0001	0.7449	1.0957

Confidence Interval Estimate
Data
X Value	13.4
Confidence Level	95%
Intermediate Calculations
Sample Size	6
Degrees of Freedom	4
t Value	2.776445
XBar, Sample Mean of X	13.28333
Sum of Squared Differences from XBar	1.568333
Standard Error of the Estimate	0.079116
h Statistic	0.175345
Predicted Y (YHat)	12.0407
For Average Y
Interval Half Width	0.0920
Confidence Interval Lower Limit	11.9487
Confidence Interval Upper Limit	12.13268
For Individual Response Y
Interval Half Width	0.2381
Prediction Interval Lower Limit	11.8026
Prediction Interval Upper Limit	12.27884

Answer for 1% level of significance to test the claim that ρ > 0 is

t	17.84
critical t	3.75

Find a 95% confidence interval for y when x = 13.4 (thousand dollars). (Use 2 decimal places.)

lower limit	11.95
upper limit	12.13

Answer for a 1% level of significance to test the claim that β > 0 is

t	14.57
critical t	3.75

Find a 95% confidence interval for β and interpret its meaning. (Use 2 decimal places.)

lower limit	0.75
upper limit	1.10