Question

The table shows the wind speed y (in mph) of a hurricane versus the barometric pressure x (in mb) Wind Barometric Pressure (mb) (x) | Speed (mph) (y) 1010 35 40 1000 1000 52 997 64 983 80 100 970 952 112 932 148 910 168 (a) Use the data in the table to find the least-squares regression line. Round the slope to two decimal places and the y-intercept to the nearest whole unit. (b) Use a graphing utility to graph the regression line and the observed data, then choose the correct graph from the options below. (c) Use the model in part (a) to approximate the wind speed of a hurricane with barometric pressure of 920 mb. Round to the nearest mph

Answer 1

a. Sum of X = 8754
Sum of Y = 799
Mean X = 972.6667
Mean Y = 88.7778
Sum of squares (SS_X) = 9602
Sum of products (SP) = -12922.6667

Regression Equation = ŷ = bX + a

b = SP/SS_X = -12922.67/9602 = -1.35

a = M_Y - bM_X = 88.78 - (-1.35*972.67) = 1398

ŷ = -1.35X + 1398

b.

180 130 80 30 960 990 1020 900 930 X-Independent C

c. Here

ŷ = -1.35X + 1398

So for x=920,

ŷ = (-1.35*920) + 1398=156