Question

too late to do something about that and Condu- parts are cach worth 4 points). B A Allowing paired dataset, with the given statistics (Part B is worth points, and the other с D E F Н 1 61 66 72 74 76 140 155 119 145 197 150 Subject p co 68 Helight 70 tical 84 95 Weight 175 Al Construct the scatterplot. Add to it the line of first fit and label this line y. Then plot the centroid, y) and label it M. STATS: P = 0.7586, X = 68, y = 140, 5, 5.5, 5, = 36.1 -4 Irela Hot he! nd HB F 199+ WEIGHT (pounds) #2 sit 72 160 ER GY 66. 6B 70 72 zy HEIGHT (inches)

Answer 1

a) From the given data Scatter Plot:

Scatterplot of Weight vs Height 200 175 150 Weight 125 100 . 60 62 64 66 68 70 72 74 76 78 Height

b) Critical Region:

Distribution Plot T, df=7 0.4 0.3 Density 0.2 0.1 0.01 0.01 0.0 -2.998 2.998 0 х

Test for correlation coefficient:

H :p=0 HA: p=0 where p corresponds to the population correlation. The sample size is n=9, so then the number of degrees of freedom is df = n - 2 = 9 – 2 = 7 The corresponding t-statistic to test for the significance of the correlation is: t=r1 n - 2 1-p2 0.7586 9 - 2 1 -0.75862 = 3.08 The p-value is computed as follows: p= Pr(|t7>3.08) = 0.0178 Since we have that p=0.0178 <0.02, it is concluded that the null hypothesis Ho is rejected. Therefore, based on the sample correlation provided, it is concluded that there is enough evidence to claim that the population correlation p is different than 0, at the 0.02 significance level.

Test Statistic t = 3.08

since t value is not in t critical value so we reject Null hypothesis.

P-value is all the area under the distribution that appears left of 0.008908 and right of 0.008908. This test carries with it is 98% confidence.

c) Regression Equation:

S.No.	Height(X)	Weight(Y)	X^2	Y^2	XY
1	60	84	3600	7056	5040
2	62	95	3844	9025	5890
3	64	140	4096	19600	8960
4	66	155	4356	24025	10230
5	68	119	4624	14161	8092
6	70	175	4900	30625	12250
7	72	145	5184	21025	10440
8	74	197	5476	38809	14578
9	76	150	5776	22500	11400
Total:	612	1260	41856	186826	86880

Mean i = 72 612 9 68 Meani 1260 9 140 byx ηΣ - (Σκ) Σν) nΣx - (Σx) 9. 86880 - 612 - 1260 9. 41856 - (612)? 781920 - 771120 376704 - 374544 Ξ 10800 2160 - 5

Regression Line y on x y- j = byx(x - 1) y - 140 = 5(x - 68) y - 140 = 5x - 340 y = 5x - 340 + 140 y = 5x - 200

Slope = 5

Y-intercept = -200

The regression equation is Y = 5X - 200

d) Scatter plot with regression

Scatterplot of Weight vs Height 200 175 150 Weight 125 100 60 62 64 66 68 70 72 74 76 78 Height

e) Correation determination r2 = 0.75862 = 0.5755

f) The residual for subject E is

Height(X)	Weight(Y)	Ycap	(Y-Ycap)^2
26	235	241.1562	37.8986336
27	273	252.6917	412.427716
41	387	414.1886	739.222198
29	253	275.7627	518.139486
33	295	321.9047	723.861016
34	335	333.4402	2.43309374
36	395	356.5112	1481.3911
45	475	460.3306	215.190451
22	203	195.0142	63.7730211
		total:	4194.33671

E = 4194.33671

G) Given X = 69 the

Y-hat = 5(69) - 200= 145