Question

Using the data above I have to answer the questions below

It’s a decreasing relationship between X=age and Y= muscle mass

SPSS only to get t A / 48 / 42 / 47 / 43 | 44 | 42 | SS | 57 | S6| 59| 57 | S41 43 44 42 M.M 102 107 107 102 115 101 87 91 97 82 78 95 102 115 101 A = Age, M.М. Muscle Mass bu tand Spss Obtain the estimated regression function. Plot the estimated regression function and the data. Does a linear regression function appear to give a good fit here? Does your plot support the anticipation that muscle mass decreases with age? 10 Marks Obtain the following 1.5 i. a point estimate of the difference in the mean muscle mass for women dif fering in age by one year 2 Marks] ii, a point estimate of the mean muscle mass for women aged X-45 years 2 Marks 3 Marks PIC.COLLAGE ii the value of the residual for the eighth case. iv, a point estimate of the error variance.

Answer 1

data

x	y
48	102
42	107
47	107
43	102
44	115
42	101
55	87
57	91
56	97
59	82
57	78
54	95
43	102
44	115
42	101

excel

data -> data analysis -> regression

result

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.807968406
R Square	0.652812946
Adjusted R Square	0.626106249
Standard Error	6.602727568
Observations	15
ANOVA
	df	SS	MS	F	Significance F
Regression	1	1065.651853	1065.651853	24.44379245	0.000268246
Residual	13	566.7481473	43.59601133
Total	14	1632.4
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	163.2969704	13.15625317	12.41211827	1.39236E-08	134.8746134
x	-1.319856146	0.26695761	-4.944066388	0.000268246	-1.896583
RESIDUAL OUTPUT
Observation	Predicted y	Residuals
1	99.94387533	2.056124673
2	107.8630122	-0.863012206
3	101.2637315	5.736268527
4	106.5431561	-4.543156059
5	105.2232999	9.776700087
6	107.8630122	-6.863012206
7	90.7048823	-3.704882302
8	88.06517001	2.934829991
9	89.38502616	7.614973845
10	85.42545772	-3.425457716
11	88.06517001	-10.06517001
12	92.02473845	2.975261552
13	106.5431561	-4.543156059
14	105.2232999	9.776700087
15	107.8630122	-6.863012206

a) this is the slope = -1.3199

b)

x = 45
y^= 163.2970 -1.3199* x
= 163.2970 -1.3199* 45
= 103.9015

c) residual for 8th case
= 2.9348

d) point estimate for error variance = MSE = 43.596