Question

Normal inches) Shoe length 11.5 10.5 105 10.5 10.5

Answer 1

N	Height (x)	Shoe length (y)	x^2	y^2
1	69	11.5	4761	132.25
2	68	10.5	4624	110.25
3	66	10.5	4356	110.25
4	55	10	3025	100
5	65	11	4225	121
6	72	13	5184	169
7	63	10.5	3969	110.25
8	64.5	10	4160.25	100
9	61	9.5	3721	90.25
10	64	11	4096	121
11	65	10.5	4225	110.25
12	69	12	4761	144
13	64	10.5	4096	110.25
14	64	13	4096	169
15	65	10	4225	100
16	67	11	4489	121
17	62	10.5	3844	110.25
18	70	11.5	4900	132.25
19	65	11	4225	121
20	64	11	4096	121
21	65	10	4225	100
22	65	10.5	4225	110.25
23	63	10.5	3969	110.25
24	66	11.5	4356	132.25
25	76	11.5	5776	132.25
26	68	12	4624	144
27	61	10	3721	100
28	75	12	5625	144
29	67	13	4489	169
30	65	11	4225	121
Total	1973.5	330.5	130313.3	3666.25

1.  

| 45 50 55 60 65 7 0 75 80

x-axis - Height

y -axis - Shoe length

Correlation coefficient (r) seems to be positive since the points are sloping upward. Therefore we can say that one variable will lead to increase in other if itself increases.

2. r =

η Σy - ΣιΣΗ (η Στ2 – (Στ)2)(nΣy – Συ)2)

= 0.59

Test Stat = $\frac{1}{2}ln(\frac{1+r}{1-r})$

= 0.6777

critical value at 0.05

=

tn-2,0/2

=

t28,0.025

= 2.0484

Since Test sTat < C.V.

We do not reject the null hypothesis and conclude that there is significantly no correlation between the height and show length.

  

3. $R^2=r^{2}$

= (0.59* 0.59)

R = 0.348 = 34.8%

34.8% of variation in shoe length is explained by the height.

It is not very good fit for the data.

4.

Regression eq of Y on X

y = a + bir

WhereSlope 'b' =

ηΣ zy –ΣΣ (η Στ2 – (Στ)2)

= 0.1339

Intercept 'a' =

y – bł

   = 2.2058

Therefore the eq is

$ = 2.2058 +0.1339x

5. Slope = 0.1339 therefore an increase in height by 1 inch will lead to increase in shoe length by 0.1339 units.

6. y-intercept is the starting point of 'y' (shoe length ) when 'x=0' (height is 0 inches). It is not meaningful because we do not have a '0' inch height.

7.

y = 0.1339x + 2.2058 45 50 55 60 65 70 75 80

8. WE can not use the line to make predictions because the correlation is not that strong and the coefficient of determination (R^2) is also very low.

9. x = 64 inch

Therefore

y = 2.2058 + 0.1339 * 64

$ = 10.7754

10. It is wrong because the regression model for this data is not very good due to low coefficient of determination and also there is some possibility of outliers.