Question

The Oklahoma State Department of Motor Vehicles needs to predict the number of new license plates that will be needed next year. The number of immigrants to the state is thought to be a good variable on which to base predictions. A regression of new plates issued in a year (Y) on the number of immigrants to the state in the same year (X) for the last 50 years shows the following results:

Ŷ = 57162 + 1.27X r2 = .31 Sy|x = 25627 sb = .80 = 15,000 sx = 5000

Based on these results, answer the following questions:

(a) Immigration to Oklahoma next year is expected to be 34,894. What is the best prediction of the number of new license plates that will be needed? Place a 95 percent confidence limit around your estimate.

(b) How good a predictor of new license plates is immigration into the state?

Answer 1

Solution:

Here in this question, Independent Variable(X) is Number of Immigrants.

Dependent Variable(Y) is Number of new licence plates.

Part(a):

Given Regression line :

Y=57162+1.27X

Where Y =number of new licence plates

             X =number of Immigrants.

Immigration to Oklahoma next year is expected to be 34,894

For X=34894

Y=57162+(1.27*34894)

= 57162+44315.38

= 101477.38

best prediction of the number of new license plates = 101477.38

Part(b):

given regrssion line:

Y=57162+1.27X

R Square =0.31

Here , in regression analysis ,we look the R-Square =0.31

It tells us how good is the fit.

It means that we are able to explain 31% of variability in Dependent variable(Number of new licence plates) from Independent variable(Number of Immigrants).