Question

2.         Complete the following in regard to the footlength and height categories of the data set:                                                                                                     

a.   In the region to the right, produce a scatterplot of the height versus footlength data (remember this means footlength runs along the horizontal axis as the independent variable and height along the vertical axis as the dependent variable.)  Based upon your scatterplot, briefly discuss below your thoughts on whether the “visual” trend between the individuals’ footlength and height appears linear, curvilinear, or has no general trend at all.                                                                                      

b.  Complete the following:                                                                                      

      i.           Include the trend line's graph and equation on the scatterplot created in part a.  Give the line's equation below and explain within this context what the "x" and "y" variables represent in the equation.                                                                                

ii.         Below, explicitly state the slope of your trend line and discuss what the value of the slope signifies in terms of this context.   

c.          Determine the value of the correlation coefficient (r) for this paired data.  Explain what this value tells you regarding these two variables.  Determine the value of the coefficient of determination (r^2) for this paired data.  Explain what this value tells you regarding these two variables.                                                                    

d.         Using the predicition equation from part bi. above, predict the height of an individual whose footlength is 24.5 cm.                                                                   

e.         Finally, critique the statement “since the correlation coefficient is statistically significant then this means that having a long foot causes one to be tall.”  Specifically, address the issue of “causation” in relation to significant statistical correlation.

Foot Length	Height
24.5	162.5
25.5	175.5
23	160
25.5	175
24	158
25	163
31	186
24.5	165
21	155
23	165
25.5	172
27	168
27	175.5
22.5	158
27	188.5
24.5	162.5
31	183
26	162.5
29	180.5
24	171
28	180.5
26	180.5
26.5	176
24	175
27	173
25.5	165.5
24	160
24	161.5
25	174
24.5	165
27.5	178
20	164
20.5	153
24	183
21.5	162.5
32	178
25	178
25	168.5
23.5	162.5
27.5	185.5
27.5	176.5
27	188
23	167
23	155
22.5	160.5
27	173
28	177.5
28	180
26.5	178
25	171.5
24	168
23	164.5
25	170.5
23	168
22	160.5
23.5	165
21	157
24	161.5
23.5	157.5
28	173

Answer 1

a.

From scatter plot we observe that as Foot length increases then height also increases hence there exists positive association between Foot length and height and hence there exists linear trend between Foot length (say x) and Height (say y).

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.770497132
R Square	0.593665831
Adjusted R Square	0.586660069
Standard Error	5.856149514
Observations	60
ANOVA
	df	SS	MS	F	Significance F
Regression	1	2906.10308	2906.103	84.73966	6.08661E-13
Residual	58	1989.080254	34.29449
Total	59	4895.183333
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	99.6934476	7.64422055	13.04168	6.83E-19	84.39187767	114.995018
X Variable 1	2.789769684	0.303057474	9.205415	6.09E-13	2.183134239	3.39640513