Question

Consider the following table summarizing the speed limit of a certain road and the number of accidents occurring on that road in January.

Posted Speed Limit 58 49 44 36 22 24

Reported Number of Accidents 28 26 22 15 18 14

1) Find the slope of the regression line predicting the number of accidents from the posted speed limit.Round to 3 decimal places.

2) Find the intercept of the regression line predicting the number of accidents from the posted speed limit. Round to 3 decimal places.

3) Predict the number of reported accidents for a posted speed limit of 21mph. Round to the nearest whole number.

Answer 1

1.

Sum of X = 233
Sum of Y = 123
Mean X = 38.8333
Mean Y = 20.5
Sum of squares (SS_X) = 1008.8333
Sum of products (SP) = 361.5

Regression Equation = ŷ = bX + a

So slope is b = SP/SS_X = 361.5/1008.83 = 0.358

2. Hence intercept is a = M_Y - bM_X = 20.5 - (0.36*38.83) = 6.585

3. So the regression equation is

ŷ = 0.358X + 6.585

Hence x=21, ŷ = (0.358*21) + 6.585=14.103=14