Question

#19: Lemons and car crashes using the listed lemon/crash data, find the best predicted crash fatality rate for a year in which there are 500 metric tons of lemon imports. Is the predication worthwhile?

Lemon Imports	230	265	358	480	530
Crash Fatality rate	15.9	15.7	15.4	15.3	14.9

Answer 1

Let x be the lemon imports in metric tons.

Let y be the crash fatality rate.

The calculation table is shown below:

Serial No.	x	y	x^2	y^2	xy
1	230	15.9	52900	252.81	3657
2	265	15.7	70225	246.49	4160.5
3	358	15.4	128164	237.16	5513.2
4	480	15.3	230400	234.09	7344
5	530	14.9	280900	222.01	7897
Total	1863	77.2	762589	1192.56	28571.7

Here, n = 5.

The simple regression model is given by,

y = a + bx   ----(1)

First calculate slope (b) and intercept (a) as shown below:

Now substitute the values in equation (1), we get

y = 16.4833 – 0.0028x

The best predicted crash fatality rate for a year in which there are 500 metric tons of lemon imports can be calculated as,

y = 16.4833 – 0.0028x

y = 16.4833 – 0.0028(500)

y = 16.4833 – 1.4

y=15.0833

Therefore, the best predicted crash fatality rate for a year in which there are 500 metric tons of lemon imports is 15.0833.

We will calculate the coefficient of determination (R2) to determine whether the predication is worthwhile or not as R2 considered as accuracy measure for regression model.

Since, the R2 value 0.92 which is close to 1, so it can be said that the accuracy of the above model is high.

Also, R2 value can be interpreted as that 92% of variations in crash fertility rate is explained by the lemon reports.

Therefore, it can be said that the predication is worthwhile.