The administrator of a school board in a large county was analyzing the average mathematics test scores in the schools under her control. She noticed that there were dramatic differences in scores among the schools. In an attempt to improve the scores of all the schools, she isolated factors that could account for the differences and were easily obtained from HR. Accordingly, she took a random sample of 40 schools across the county and for each determined: Test Score, Y: the mean test score last year at the school sampled Math Dgr, X1: the percentage of teachers in each school who have at least one university degree in math Age, X2: the mean age of the math teachers at the school sampled Income, X3: the mean annual income of the math teachers at the school sampled Data: Test Score Math Dgr Age Income 73.9 77 52 44.4 59.4 48 32 49 64.6 33 50 52.6 59.8 25 43 39.6 58.8 25 40 40.7 58.7 39 33 38 68.5 71 37 25.1 54.7 24 48 46.5 61.7 25 47 38.4 81.6 49 50 44.6 83.7 56 59 54.8 62.5 46 40 38.5 68.2 75 41 44.8 51.1 25 51 39.9 44 46 38 55.6 65.7 68 45 44.1 69.6 27 49 47.5 54.5 23 31 40 56.5 48 38 40.2 44.8 41 38 28.3 72.6 79 39 44.8 65.3 76 43 34.5 64.9 31 39 28 69.8 63 49 51.4 75.3 72 49 55.2 57 30 23 24.6 52.8 62 34 29.7 71.3 75 36 32.1 55.2 43 35 32.6 62.6 64 50 37.4 58.2 44 45 42.9 71.8 46 29 34.4 69.9 35 39 45.6 70.1 63 34 52.9 66.1 56 36 22.1 71.7 57 59 55.1 68.8 41 40 33.7 45 27 40 19.8 61.9 37 44 48.2 56 36 56 55.9 The least squares regression equation using the percentage of teachers with a math degree to predict mean test score is given by: predicted Math Score = 50.65 + 0.2634(MathDgr%) Estimate a school’s predicted mean test score given that 30% of the math teachers have at least one university math degree. (Be sure to use the correct units as they are recorded in the dataset for inputting 30%).

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Description: The administrator of a school board in a large county was analyzing the average mathematics test scores in the schools under her control. She noticed that there were dramatic differences in scores among the schools. In an attempt to improve the sco

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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The administrator of a school board in a large county was analyzing the average mathematics test scores in the schools under her control. She noticed that there were dramatic differences in scores among the schools. In an attempt to improve the scores of all the schools, she isolated factors that could account for the differences and were easily obtained from HR. Accordingly, she took a random sample of 40 schools across the county and for each determined:

Test Score, Y: the mean test score last year at the school sampled

Math Dgr, X1: the percentage of teachers in each school who have at least one university

degree in math

Age, X2: the mean age of the math teachers at the school sampled

Income, X3: the mean annual income of the math teachers at the school sampled

Data:

Test Score	Math Dgr	Age	Income
73.9	77	52	44.4
59.4	48	32	49
64.6	33	50	52.6
59.8	25	43	39.6
58.8	25	40	40.7
58.7	39	33	38
68.5	71	37	25.1
54.7	24	48	46.5
61.7	25	47	38.4
81.6	49	50	44.6
83.7	56	59	54.8
62.5	46	40	38.5
68.2	75	41	44.8
51.1	25	51	39.9
44	46	38	55.6
65.7	68	45	44.1
69.6	27	49	47.5
54.5	23	31	40
56.5	48	38	40.2
44.8	41	38	28.3
72.6	79	39	44.8
65.3	76	43	34.5
64.9	31	39	28
69.8	63	49	51.4
75.3	72	49	55.2
57	30	23	24.6
52.8	62	34	29.7
71.3	75	36	32.1
55.2	43	35	32.6
62.6	64	50	37.4
58.2	44	45	42.9
71.8	46	29	34.4
69.9	35	39	45.6
70.1	63	34	52.9
66.1	56	36	22.1
71.7	57	59	55.1
68.8	41	40	33.7
45	27	40	19.8
61.9	37	44	48.2
56	36	56	55.9

The least squares regression equation using the percentage of teachers with a math degree to predict mean test score is given by:

predicted Math Score = 50.65 + 0.2634(MathDgr%)

Estimate a school’s predicted mean test score given that 30% of the math teachers have at least one university math degree. (Be sure to use the correct units as they are recorded in the dataset for inputting 30%).

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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