Question

Following are age and price data for 8 randomly selected ambulances between 1 and 6 years old.​ Here, x denotes​ age, in​ years, and y denotes​ price, in hundreds of dollars. Use the information to do parts​ (a) through​ (d).

x 6    1    6 2 6 2 4 5

y 280    420 275    360    265    350    325    305

Summation from nothing to nothing x equals 32 ∑x=32​, Summation from nothing to nothing y equals 2580 ∑y=2580​, Summation from nothing to nothing xy equals 9585 ∑xy=9585​, Summation from nothing to nothing x squared equals 158 ∑x2=158

a. Compute​ SST, SSR, and​ SSE, using the​ formulas,

SST = ________ ​(Round to two decimal places as​ needed.)

b. compute the coefficient of determination, r2.

c. Determine the percentage of variation in the observed values of the response variable explained by the regression, and intrepret you answer.

d.State how useful the regression equation appears to be making predictions

Answer 1

Soluion:

install analysis tool pak in excel

Go to data>data analysis>Regression

You will get follwo output:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.964687
R Square	0.93062
Adjusted R Square	0.919057
Standard Error	14.95828
Observations	8
ANOVA
	df	SS	MS	F	Significance F
Regression	1	18007.5	18007.5	80.48045	0.000107
Residual	6	1342.5	223.75
Total	7	19350
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	420.5	12.13681	34.64667	3.85E-08	390.8023	450.1977
x	-24.5	2.730995	-8.97109	0.000107	-31.1825	-17.8175

Coming to answers:

SST=19350

SSR=18007.5

SSE=1342.5

Solutionb:

rsq=0.9306

Solutionc:

r sq=0.9306

0.9306*100=93.06% variation in y is explained by model.

Good model.

Solutiond:

we can predict price with the given age of ambulance.

Also from ANOVA

F(1,6)=80.4805

p=0.0001

p<0.05

Model is significant and can be used for prediction.