Question

number 9

An experimenter studied the effect of speed (mph) is relation to stopping distance (feet). The data is summarized below. (3-9) Speed, mph (x) 50 52 60 55 65 80 45 Stopping distance (feet) 257 264 274 266 277 320 250 3. Sketch a scatter plot for these data. 4. This problem is an example of a a normally distributed variable b. test for independence c. Goodness of Fit test Focus MacBook Pro

Answer 1

Solution:

9)

X	Y	XY	X2	Y2
50	257	12850	2500	66049
52	264	13728	2704	69696
60	274	16440	3600	75076
55	266	14630	3025	70756
65	277	18005	4225	76729
80	320	25600	6400	102400
45	250	11250	2025	62500
407	1908	112503	24479	523206

Slope of line is

b = ΠΣxy - (Σx)(ΣΥ) ΠΣχ2 - (Σx)2

b = 1.9223

y intercept is

a = 160.8014

The equation of the regression line is

$\hat y$ = a + bx

i.e. $\hat y$ =  160.8014 + 1.9223 x

Put x = 70 and find y

y = 160.8014 + (1.9223 * 70) =  295.3624

Answer :  295.3624 feet