Statistics project
Order Instructions:
For this project you are to conduct an Experiment. You will need to provide a detailed description
of your project, highlighting how the data were obtained, the variables used (including units), and
your objective. Your project needs to be typed and plots can be made using any software of your
choice. Only one project (with each member’s name) per group needs to be submitted. After
providing the description, please answer in detail the four questions below. Your project should
include all the observations used.
1. (25%) State your experiment’s objective in terms of the Null and Alternative Hypotheses.
2. (25%) Test your Null hypothesis at the 5% level of significance. Make sure to check that all the
conditions/assumptions have been met.
3. (25%) Construct a 90% confidence interval for the parameter of your null hypothesis.
4. (25%) What is the probability that you observe a value of 0 that is 1 standard deviation greater
than your estimated value (based on your sample) of the parameter.
SAMPLE ANSWER
Statistics project
Introduction
Following the recent trend on the global systolic blood pressure, it became imperative to conduct an experiment with an aim of identifying the factors that cause blood pressure. As a result, an experiment was conducted to identify whether age in years and weight in pounds are significant predictors of an individual’s systolic blood pressure. It is notable that it was important to use data collected from secondary sources because of the difficulties involved in collecting data for some variables. Simply put, it is difficult to collect data on the systolic blood pressure (manually) of individuals because of the instruments used in measuring the same variable. It is undeniable that only professionals in the health and medical industry have the capacity to collect data on systolic blood pressure. It follows that data used for the upcoming analysis was retrieved from (http://college.cengage.com, n.p). This paper uses multiple regression analysis to identify whether age in years and weights in pounds are significant predictors of an individual’s systolic blood pressure.
State your experiment’s objective in terms of the Null and Alternative Hypotheses
In order to complete the experiment successfully, the null and alternative hypotheses were used. In simple terms:
H_{0}: Age in Years and weight in pounds are not significant predictors of systolic blood pressure.
Against
H_{1}: Age in Years and weight in pounds are significant predictors of systolic blood pressure.
Test your Null hypothesis at the 5% level of significance. Make sure to check that all the
conditions/assumptions have been met.
It is crucial to point out that the following assumptions were made.
Assumption 1: for i=1, 2…N. this assumption could be understood as the expectation
for the error terms or deviations is assumed to be zero.
Assumption 2: for i=1, 2…N. That is, the variance of the error terms is constant.
This assumption is termed as homoscedasticity, or homogeneity of variances.
Assumption 3: . This could be explained as the error terms have a normal distribution with mean zero and variance.
Assumption 4: There is a linear relationship between the independent variable and the
independent variables.
The following graphs were used to check for the assumptions made in the analysis.
Assumption 1 and 2
It can be seen that the number of observations are balanced in both graphs i.e. the number of observations above and below tend to balance. This implies that taking the average of the error terms will almost be equal to zero (Montgomery, 78). It is also evident the distance from the line Zero does not have any outliers in both graphs. This is an indication that the data has a constant variance.
Assumption 3
The normal probibility plot above clearly indicates that both age in years and weight in pounds follows a normal distribution (Montgomery, 78). Thus the third assumption is fullfilled.
Assumption 4
The plots indicate that both age in years and the weight in pounds have a linear relationship with systolic blood pressure (Montgomery, 79). This is highlighted by the reality that the observations fit on a straight line.
Construct a 90% confidence interval for the parameter of your null hypothesis.
The null hypothesis for the 90 percent confidence interval is that the y intercept minus the coefficient for age minus the coefficient for weight is equal to zero at α=0.10. The following output was obtained after running a multiple linear regression on age and weight on the systolic blood pressure.
Regression Statistics | |||||
Multiple R | 0.988356 | ||||
R Square | 0.976847 | ||||
Adjusted R Square | 0.971059 | ||||
Standard Error | 2.318211 | ||||
Observations | 11 | ||||
ANOVA | |||||
df | SS | MS | F | Significance F | |
Regression | 2 | 1813.916 | 906.9581 | 168.7646 | 2.87357E-07 |
Residual | 8 | 42.99282 | 5.374103 | ||
Total | 10 | 1856.909 |
Coefficients | Standard Error | t Stat | P-value | Lower 90.0% | Upper 90.0% | |
Intercept | 30.9941 | 11.9438 | 2.5950 | 0.0319 | 8.7841 | 53.2041 |
Age in Years | 0.8614 | 0.2482 | 3.4702 | 0.0084 | 0.3998 | 1.3230 |
Weight in Pounds | 0.3349 | 0.1307 | 2.5627 | 0.0335 | 0.0919 | 0.5778 |
What is the probability that you observe a value of zero that is one standard deviation greater than your estimated value (based on your sample) of the parameter.
From the output above it is clear that the probability of observing zero for age in years is 0.0084. The probability of observing zero for the y intercept is 0.0319 and for weight in pounds is 0.0919. Considering, the level of significance of all the variables, it is evident to conclude that both age and weight are significant predictors of systolic blood pressure. This owes to the reality that both variables have p values, which are less than 0.05.
In conclusion, this paper uses multiple linear regression analysis to identify whether age in years and weights in pounds are significant predictors of an individual’s systolic blood pressure. It is evident that both age and weight are significant predictors of systolic blood pressure.
Works Cited
Montgomery, Douglas C. Introduction to Linear Regression Analysis. Oxford: Wiley-Blackwell, 2011 Print.
Systolic Blood Pressure Data. (n.d). Web. 9 June 2014.
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