Question
In: Statistics and Probability
Check that the measurements for the heart rate are coming from a normal distribution by constructing...
- Check that the measurements for the heart rate are coming from a normal distribution by constructing a histogram.
- Create indicator variables for female and good AQI. Fit the regression model and discuss its goodness of fit. What portion of variation in heart rate can this model explain?
- Write the fitted model. What variables are significant predictors of heart rate at the 5% level of significance?
- Plot residuals against predicted values. Does it show any pattern?
- Compute the predicted heart rate of a 50-year-old male who has a BMI of 20, is not taking any heart medications, and resides in an area with a good air quality
A cardiologist conducts a study to find out what factors are good predictors of elevated heart rate (HR) in her patients. She measures heart rate at rest in 30 patients on their next visit, and obtains from the medical charts additional information on their age, gender, body mass index (BMI), and the number of currently taken heart medications. She also obtains the air quality index (AQI) for area of residence of her patients (unhealthy or good). The data are given in the file
| age | gender | BMI | nmeds | AQI | HR |
| 69 | M | 24.1 | 2 | unhealthy | 94 |
| 54 | M | 29.6 | 0 | unhealthy | 92 |
| 57 | F | 20.2 | 2 | good | 81 |
| 71 | F | 21.5 | 2 | good | 100 |
| 62 | M | 27.4 | 3 | good | 79 |
| 58 | M | 18.9 | 2 | good | 79 |
| 65 | F | 22.2 | 1 | good | 106 |
| 70 | F | 25.9 | 1 | unhealthy | 117 |
| 67 | F | 23.4 | 1 | good | 94 |
| 63 | M | 23.8 | 2 | unhealthy | 108 |
| 55 | M | 24.6 | 0 | good | 94 |
| 64 | F | 31.4 | 3 | good | 97 |
| 63 | M | 28 | 2 | good | 91 |
| 66 | M | 22.9 | 2 | good | 86 |
| 44 | F | 17.2 | 0 | unhealthy | 86 |
| 53 | M | 25.2 | 0 | good | 84 |
| 71 | F | 20.3 | 2 | unhealthy | 111 |
| 49 | M | 17.1 | 1 | good | 75 |
| 65 | F | 23.4 | 2 | unhealthy | 114 |
| 45 | F | 19 | 2 | unhealthy | 83 |
| 56 | F | 22.9 | 3 | unhealthy | 112 |
| 74 | M | 32.4 | 1 | good | 97 |
| 48 | F | 29.9 | 0 | good | 76 |
| 50 | F | 23.9 | 1 | unhealthy | 97 |
| 66 | F | 27.8 | 3 | good | 82 |
| 73 | F | 24.8 | 3 | good | 105 |
| 61 | M | 32.8 | 1 | good | 84 |
| 82 | M | 29.7 | 0 | good | 92 |
| 72 | F | 25.2 | 0 | good | 114 |
| 59 | F | 22.6 | 0 | good |
86 |
Solutions
Expert Solution
|
Descriptive Statistics |
|||
|
Mean |
Std. Deviation |
N |
|
|
HR |
93.8667 |
12.37833 |
30 |
|
Age |
61.7333 |
9.32528 |
30 |
|
Gender |
.4333 |
.50401 |
30 |
|
AQI |
.6667 |
.47946 |
30 |
|
BMI |
24.6293 |
4.26183 |
30 |
heart rate (HR) on average 93.8667 of patients. On average age 61.7333 of patients.
|
Correlations |
||||||
|
HR |
Age |
Gender |
AQI |
BMI |
||
|
Pearson Correlation |
HR |
1.000 |
.505 |
-.361 |
-.438 |
.025 |
|
Age |
.505 |
1.000 |
.047 |
.234 |
.360 |
|
|
Gender |
-.361 |
.047 |
1.000 |
.190 |
.267 |
|
|
AQI |
-.438 |
.234 |
.190 |
1.000 |
.268 |
|
|
BMI |
.025 |
.360 |
.267 |
.268 |
1.000 |
|
|
Sig. (1-tailed) |
HR |
. |
.002 |
.025 |
.008 |
.447 |
|
Age |
.002 |
. |
.402 |
.107 |
.025 |
|
|
Gender |
.025 |
.402 |
. |
.157 |
.077 |
|
|
AQI |
.008 |
.107 |
.157 |
. |
.076 |
|
|
BMI |
.447 |
.025 |
.077 |
.076 |
. |
|
|
N |
HR |
30 |
30 |
30 |
30 |
30 |
|
Age |
30 |
30 |
30 |
30 |
30 |
|
|
Gender |
30 |
30 |
30 |
30 |
30 |
|
|
AQI |
30 |
30 |
30 |
30 |
30 |
|
|
BMI |
30 |
30 |
30 |
30 |
30 |
Heart Rate to BMI and age as positive correlation.
Heart Rate to Gender and AQI are perfect positive correlation.
|
Model Summaryb |
||||||||||
|
Model |
R |
R Square |
Adjusted R Square |
Std. Error of the Estimate |
Change Statistics |
Durbin-Watson |
||||
|
R Square Change |
F Change |
df1 |
df2 |
Sig. F Change |
||||||
|
1 |
.814a |
.663 |
.609 |
7.73649 |
.663 |
12.310 |
4 |
25 |
.000 |
2.234 |
|
a. Predictors: (Constant), BMI, Gender, AQI, Age |
||||||||||
|
b. Dependent Variable: HR |
R_Squre = 0.663
66.3% indicates that the model explains all the variability of the HR data around its mean.It's mean's that the model is good fit for the heart rate data.
|
ANOVAa |
||||||
|
Model |
Sum of Squares |
df |
Mean Square |
F |
Sig. |
|
|
1 |
Regression |
2947.134 |
4 |
736.784 |
12.310 |
.000b |
|
Residual |
1496.332 |
25 |
59.853 |
|||
|
Total |
4443.467 |
29 |
||||
|
a. Dependent Variable: HR |
||||||
|
b. Predictors: (Constant), BMI, Gender, AQI, Age |
|
Coefficientsa |
|||||||||||
|
Model |
Unstandardized Coefficients |
Standardized Coefficients |
t |
Sig. |
95.0% Confidence Interval for B |
Correlations |
|||||
|
B |
Std. Error |
Beta |
Lower Bound |
Upper Bound |
Zero-order |
Partial |
Part |
||||
|
1 |
(Constant) |
52.661 |
11.034 |
4.773 |
.000 |
29.936 |
75.386 |
||||
|
Age |
.847 |
.168 |
.638 |
5.054 |
.000 |
.502 |
1.192 |
.505 |
.711 |
.587 |
|
|
Gender |
-7.216 |
2.991 |
-.294 |
-2.413 |
.024 |
-13.377 |
-1.056 |
-.361 |
-.435 |
-.280 |
|
|
AQI |
-13.833 |
3.177 |
-.536 |
-4.354 |
.000 |
-20.377 |
-7.289 |
-.438 |
-.657 |
-.505 |
|
|
BMI |
.052 |
.380 |
.018 |
.136 |
.893 |
-.731 |
.834 |
.025 |
.027 |
.016 |
|
|
a. Dependent Variable: HR Regression model : HR = 53.388 + 0.854 *Age - 7.119 *Gender - 13.763 * AQI The predicate heart rate 53.388 as per one unit of heart rate. The predicate heart rate to age increases by 0.845 year as per one unit of heart rate. The predicate heart rate to Gender decreases by -7.119 as per one unit of heart rate. The predicate heart rate to AQI decreases by -13.763 year as per one unit of heart rate. |
|
Coefficient Correlationsa |
||||||
|
Model |
BMI |
Gender |
AQI |
Age |
||
|
1 |
Correlations |
BMI |
1.000 |
-.240 |
-.161 |
-.325 |
|
Gender |
-.240 |
1.000 |
-.138 |
.075 |
||
|
AQI |
-.161 |
-.138 |
1.000 |
-.162 |
||
|
Age |
-.325 |
.075 |
-.162 |
1.000 |
||
|
Covariances |
BMI |
.144 |
-.273 |
-.195 |
-.021 |
|
|
Gender |
-.273 |
8.947 |
-1.311 |
 orchestra answered 2 years agoRelated SolutionsSuppose that the pH measurements of the field from the question above follow a normal distribution...Suppose that the pH measurements of the field from the question
above follow a normal distribution with mean 11 pH and standard
deviation 2 pH. What is the probability that the engineer obtains a
sample mean (with n = 5) greater than 11.8 pH? Assume each
measurement is independent of each other.
Question3: Consider the following 14 independent measurements from a normal distribution: Independent measurements 20 18 11...
Question3: Consider the following 14 independent measurements
from a normal distribution:
Independent measurements
20 18 11 20 16 14 15 15 14 13 11 18 20 9
1) What is the standard error of the sample mean?
0.9936
3.5826
0.9575
3.4303
2) Calculate a 99% confidence interval for the population
mean.
[5.8831,24.6883]
[12.9734,17.5980]
[12.4015,18.1700]
[12.7480,17.8234]
If X represents a random variable coming from a normal distribution with mean 3 and if...If X represents a random variable coming from a normal
distribution with mean 3 and if P(X>4.2)=0.36P(X>4.2)=0.36,
then P(3<X<4.2)=0.14P(3<X<4.2)=0.14.
___True
___False
NORMAL DISTRIBUTION 1. 1A. Which of the following statements are TRUE about the Normal Distribution? Check...NORMAL DISTRIBUTION
1.
1A.
Which of the following statements are TRUE about
the Normal Distribution? Check all that apply.
The distribution is symmetric with a single peak.
50% of the data values lie at or above the mean.
Data values are spread evenly around the mean.
The graph of the Normal Distribution is bell-shaped, with
tapering tails that never actually touch the horizontal axis.
The mean, median and mode are all equal and occur at the center
of the distribution....
Suppose you have selected a random sample of ?=13 measurements from a normal distribution. Compare the...Suppose you have selected a random sample of ?=13 measurements
from a normal distribution. Compare the standard normal z values
with the corresponding t values if you were forming the following
confidence intervals.
a) 80% confidence interval
?=
?=
(b) 90% confidence interval
?=
?=
(c) 99% confidence interval
?=
?=
An article reports measurements of the total power, on the log scale, of the heart rate...An article reports measurements of the total power, on the log
scale, of the heart rate variability, in the frequency range 0.003
to 0.4 Hz, for a group of 40 patients aged 25–49 years and for a
group of 43 patients aged 50–75 years. The mean for the patients
aged 25–49 years was 4 with a standard deviation of 0.23, and the
mean for the patients aged 50–75 years was 3.4 with a standard
deviation of 0.28. Let μX represent...
Suppose you have selected a random sample of n =5 measurements from a normal distribution. Compare...Suppose you have selected a random sample of n =5 measurements
from a normal distribution. Compare the standard normal z values
with the corresponding t values if you were forming the following
confidence intervals.
(a) 8080% confidence interval
z=
t=
(b) 9898% confidence interval
z=
t=
(c) 9595% confidence interval
z=
t=
ConfidenceIntervals
Suppose the current measurements in a strip of wire are assumed to follow a normal distribution...Suppose the current measurements in a strip of wire are assumed
to follow a normal distribution with a mean of 10 mA and a variance
of 4 (mA)^2.
a. What is the probability that a measurement will exceed 13
mA?
b. What is the probability that a current measurement is between
9 and 11 mA?
c. Determine the value for which the probability that a current
measurement is below this value is 0.98.
Please show all steps and explanations. Thank...
a.) Viscosity measurements for a certain petroleum fraction can be modelled using a normal distribution with...a.) Viscosity measurements for a certain petroleum fraction can
be modelled using a normal distribution with a mean of 41 and a
standard deviation of 7. The 99th percentile of this distribution
is
b.) Suppose X has a normal distribution with mean 3 and standard
deviation 1. The 95th percentile of this distribution is
Group of answer choices
c.) United Airlines Flight 433 is a nonstop flight from Boston’s
Logan airport to San Francisco International Airport. An important
factor in...
a.) Viscosity measurements for a certain petroleum fraction can be modelled using a normal distribution with...a.) Viscosity measurements for a certain petroleum fraction can
be modelled using a normal distribution with a mean of 41 and a
standard deviation of 7. The 99th percentile of this distribution
is
b.) Suppose X has a normal distribution with mean 3 and standard
deviation 1. The 95th percentile of this distribution is
Group of answer choices
c.) United Airlines Flight 433 is a nonstop flight from Boston’s
Logan airport to San Francisco International Airport. An important
factor in...
ADVERTISEMENT
ADVERTISEMENT
Latest Questions
ADVERTISEMENT
|