The following data represent measures a random sample of 25 individuals with high cholesterol levels. The variables are as follows: Dependent variable Y: Systolic Blood Pressure (SBP) Independent variable X_1: Body Size, measured by Quetelet (QUET) Index 100(weight/height2) Independent variable X_2: Age ID SBP Size Age 1 135 2.876 45 2 122 3.251 41 3 130 3.1 49 4 148 3.768 52 5 146 2.979 54 6 129 2.79 47 7 162 3.668 60 8 160 3.612 48 9 144 2.368 44 10 180 4.637 64 11 166 3.877 59 12 138 4.032 51 13 152 4.116 64 14 138 3.673 56 15 140 3.562 54 16 134 2.998 50 17 145 3.36 49 18 142 3.024 46 19 135 3.171 57 20 142 3.401 56 21 150 3.628 56 22 144 3.751 58 23 137 3.296 53 24 132 3.21 50 25 149 3.301 54 Using software, carry out MLR analyses to obtain raw regression coefficients. Mean center age and QUET. Write the regression equation Interpret the intercept Interpret the slope for QUET Interpret the slope for age Interpret the hypothesis tests for each regression coefficient Report the coefficient of multiple determination obtained in your MLR analysis and interpret the associated hypothesis test. For an individual of age 51 and QUET 3.30, obtain by hand calculation the predicted level of SBP (remember they should be mean centered). If that individual’s actual SBP was found to be 130, obtain the residual.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

The following data represent measures a random sample of 25 individuals with high cholesterol levels. The variables are as follows:

Dependent variable Y: Systolic Blood Pressure (SBP)

Independent variable X_1: Body Size, measured by Quetelet (QUET) Index 100(weight/height2)

Independent variable X_2: Age

ID	SBP	Size	Age
1	135	2.876	45
2	122	3.251	41
3	130	3.1	49
4	148	3.768	52
5	146	2.979	54
6	129	2.79	47
7	162	3.668	60
8	160	3.612	48
9	144	2.368	44
10	180	4.637	64
11	166	3.877	59
12	138	4.032	51
13	152	4.116	64
14	138	3.673	56
15	140	3.562	54
16	134	2.998	50
17	145	3.36	49
18	142	3.024	46
19	135	3.171	57
20	142	3.401	56
21	150	3.628	56
22	144	3.751	58
23	137	3.296	53
24	132	3.21	50
25	149	3.301	54

Using software, carry out MLR analyses to obtain raw regression coefficients. Mean center age and QUET.
1. Write the regression equation
2. Interpret the intercept
3. Interpret the slope for QUET
4. Interpret the slope for age
5. Interpret the hypothesis tests for each regression coefficient
Report the coefficient of multiple determination obtained in your MLR analysis and interpret the associated hypothesis test.
For an individual of age 51 and QUET 3.30, obtain by hand calculation the predicted level of SBP (remember they should be mean centered). If that individual’s actual SBP was found to be 130, obtain the residual.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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