Question

**Please write the answer legibly. Thank
you.**

**The age (X) and glucose levels (Y) of 6 patients are
calculated in order to see if there is a relationship
between these two variables. The following data was
collected:
SP xy = 478
SS x = 1241
SS y = 656
Calculate the correlation coefficient using the formula: r = SPxy /
√ SSx SSy => [sq root of SSx SSy ]**

**----------------------------**

**Using the correlation coefficient (r) derived from above
and the data indicated below, determine
(1) the regression equation and (2) the standard error of the
estimate using the following formulas:
_ _
Least Squares Regression Equation: Y’ = bX + a where a = Y - bX and
b = SSy/SSx • r => sq rt of SSy/SSx**

**Standard Error of the Estimate: Sy|x = SSy (1 – r 2
)/n-2 [take sq root of entire fraction]
_
also, X = 4.2
_
Y = 81**

**------------------------------**

**Given the regression equation determined in problem
immediately above, answer the following:
A. What is the predicted glucose level of a patient whose age is
43?
B. What is the predicted glucose level of a patient whose age is
59?**

Answer #1

Calculate the correlation coefficient

r = SPxy / √ SSx SSy

r= **478 /**
sqrt(**1241*656)**

r= 0.5298

(1) the regression equation and (2) the standard error of the estimate using the following formulas:

b = SSy/SSx

b = **656/1241**

**b =
0.5286**

**a = Y –
bX**

**a = 81
-0.5286*4.2**

**a=78.7799**

**y=78.7799 +
0.5286*x**

**Given the regression
equation determined in problem immediately above, answer the
following:**

A. What is the predicted glucose level of a patient whose age is 43?

**y=78.7799 +
0.5286*x**

**y=78.7799 +
0.5286***43

**y=
101.5097**

**B.** **What is the predicted glucose level of a patient
whose age is 59?**

**y=78.7799 +
0.5286*x**

**y=78.7799 +
0.5286*59**

**y=
109.9673**

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x
2
3
3
4
1
5
y
$383
$420
$466
$547
$206
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x
17
27
37
47
57
67
77
y
39
22
22
12
10
7
5
Complete parts (a) through (e), given
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Let x be the age of a licensed driver in years. Let
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x
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47
57
67
77
87
y
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8
10
14
33
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A researcher wants to predict the finish position ( y) using the
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37-year-olds are due to failure to yield the right of way.
x
37
47
57
67
77
87
y
5
8
10
16
32
42
Complete parts (a) through (e), given Σx =...

Let x be the age in years of a licensed automobile
driver. Let y be the percentage of all fatal accidents
(for a given age) due to speeding. For example, the first data pair
indicates that 34% of all fatal accidents of 17-year-olds are due
to speeding.
x
17
27
37
47
57
67
77
y
34
28
18
12
10
7
5
Complete parts (a) through (e), given
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Σx2 = 18,263,
Σy2 =...

Let x be the age of a licensed driver in years. Let
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37-year-olds are due to failure to yield the right of way.
x
37
47
57
67
77
87
y
5
8
10
14
27
45
Complete parts (a) through (e), given Σx =...

A hypothesis test using a Pearson’s correlation coefficient is
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