9.18
a) Using forward stepwise regression to find the best subset of predictor variables to predict job proficiency. The Alpha-to-Enter significance level was set at 0.05 and the Alpha-to-Leave significance level was set at 0.10. The first predictor entered into the stepwise model is X3. SAS tells us that the estimated intercept is -106.13 and the estimated slope for X3 is 1.968. The R2-value is 0.8047, mean square error is 76.87. The second predictor entered into the stepwise model is X1. The estimated intercept is -127.596, the estimated slope for X1 is 0.3485 and the slope for X3 is 1.8232. The R2-value is 0.933 and the mean square error is 27.575. The final predictor entered is X4. The estimated intercept is -124.20, the estimated slope for X4 is 0.5174, the slope for X1 adjusts to 0.2963 and the slope for X3 adjusts to 1.357. The R2-value is 0.9615 and the mean square error is 16.581. Predictor X2 is not eligible for entry into the stepwise model because its t-test P-value doesn’t meet the 0.05 significance level. We prefer the model containing the three predictors X3, X1 and X4, because its R2-value is 0.9615, which is higher than 0.9330 (the model containing just two predictors X3 and X1) and 0.8047(the model containing just one predictor X3). Checking the mean square error of the three models we find that the model we selected as best model has the smallest mean square error 16.581, which is good. To sum up, using forward stepwise regression, the best model to predict the job proficiency is Y= -124.20 + 0.2963X1 + 1.357X3 + 0.5174X4, a model containing predictor variables X1, X3 and X4.

b) Compare the best subset obtained from forward stepwise regression with that obtained from the adjusted R-square value criterion.

Above is the SAS output of the Adjusted R-Square Selection Method. According to the adjusted R-square value criterion, the best model should be the model with...

...H5 was ruled out for the alpha being greater than the P-value for the age at which the first claim occurred.
The P-value for H1 and H3 both have an alpha level which is less than the P-value. However, we have compared how age of the patient affects H1 & H3. We have created two subsets using our independent variables. The patients in H6 are ages 0-39. H7 contains the same independent variables, however, the patients are over the age of 40. We have found that for patients aged 0-39 have a greater increase in days in the hospital as drug count and visit count increase. In comparison, patients age 40 and over spend a less number of days in the hospital.
The remainder of our analysis will focus on H6 & H7.
Methods: Descriptive Statistics
1. Demographics of Data Collection and Operationalization of the Variables
The study population consists of:
PEOPLE AGES (at the first time of service):
* 0-39 years old
DRUG COUNT: Number of Drugs Administered at First Service
VISIT COUNT: Number of hospital visits in Year 1
(See Appendix A.)
Data Syntheses: There is a definite relationship between the independent variables and the hypotheses tested. We tested a sample size (n= 8356) of patients who volunteered their information. We concluded that the strongest correlation exists between the visit count and the number of days spent in the hospital.
For H7 the P-value for visit count is .000. The P-value for drug count is .000.
Results: (n=8356)...

...
November 19, 2010
NAME: The Statistics of Poverty and Inequality
TYPE: Sample
SIZE: 97 observations, 8 variables
DESCRIPTIVE ABSTRACT:
For 97 countries in the world, data are given for birth rates, death
rates, infant death rates, life expectancies for males and females, and
Gross National Product.
SOURCES:
Day, A. (ed.) (1992), _The Annual Register 1992_, 234, London:
Longmans.
_U.N.E.S.C.O. 1990 Demographic Year Book_ (1990), New York: United
Nations.
VARIABLE DESCRIPTIONS:
Columns
1 - 6 Live birth rate per 1,000 of population
7 - 14 Death rate per 1,000 of population
15 - 22 Infant deaths per 1,000 of population under 1 year old
23 - 30 Life expectancy at birth for males
31 - 38 Life expectancy at birth for females
39 - 46 Gross National Product per capita in U.S. dollars
47 - 52 Country Group
1 = Eastern Europe
2 = South America and Mexico
3 = Western Europe, North America, Japan, Australia, New Zealand
4 = Middle East
5 = Asia
6 = Africa
53 - 74 Country
Values are aligned and delimited by blanks.
Missing values are denoted with *.
The Statistics of Poverty and Inequality
This paper describes a case study based on data taken from the U.N.E.S.C.O. 1990 Demographic Year Book and The Annual Register 1992 giving birth rates, death rates, life expectancies, and Gross National Products for 97 countries.
When reviewing the statistics...

...DEPARTMENT OF SOCIOLOGY, PSYCHOLOGY AND SOCIAL WORK
SOCI 1005 (SY16C) -INTRODUCTORY STATISTICS FOR THE
BEHAVIOURAL SCIENCES
SUMMER SCHOOL 2012/2013- COURSE OUTLINE
Lecturer: Ayesha Facey
Office: Room 46, Faculty of Social Sciences
Office #: 970-6324
E-mail: ayeshafcy@yahoo.com
COURSE OBJECTIVE
This course aims to introduce students to basic univariate and bivariate statistics. A student who successfully completes this course will possess a reasonable level of knowledge of basic statistics and their interpretations.
LEARNING OUTCOMES
At the end of the course, students should be able to:
• Adequately define statistical concepts
• Distinguish between descriptive statistics and inferential statistics
• Distinguish between qualitative data and quantitative data
• Classify data with respect to the four levels of measurement: nominal, ordinal, interval, and ratio
• Create grouped frequency distributions
• Compute measures of central tendency and variation and use them to analyze data
• Calculate and interpret the correlation coefficient and equation of the least-squares regression line for bivariate data and use the results to make predictions.
• Solve probabilities
• Compute binomial distributions
• Use the normal distribution to interpret z scores and compute probabilities
• Estimate a...

...SECTION A (You should attempt all 10 questions)
A1. Regression analysis is ____________________________________.
A) describes the strength of this linear relationship.
B) describes the mathematical relationship between two variables.
C) describes the pattern of the data.
D) describes the characteristic of independent variable.
A2. __________________ is used to illustrate any relationship between two variables.
A) Histogram
B) Pie chart
C) Scatter diagram
D) Frequency polygon
Questions A3 to A5 relate to the following information.
Suppose a firm fed the values of turnover, y, and advertising expenditure, x, (both in $000) for the past eight years, into a computer and obtained the regression relationship y = 26.7 + 8.5x.
A3. What is the dependent variable?
A) Number of computers
B) Size of the firm
C) Turnover
D) Advertising expenditure
A4. What is the independent variable?
A) Number of computers
B) Size of the firm
C) Turnover
D) Advertising expenditure
A5. If the advertising expenditure is $5000 in a particular year, estimate the turnover for that year.
A) $69,200
B) $42,526.70
C) $26.7
D) $69.20
A6. Explain what the following sample correlation coefficients tell you about the relationship between the x and y values in the sample:
r = - 0.8
A) No correlation.
B) Perfect negative...

...Chapt 10 # 42
H0: game length is >= 3.5 hours
Ha: game length is < 3.5 hours
mean = 2.9553
stdev = 0.5596
Get the t test statistic:
t = (x-mu)/(stdev/sqrt(N))
t = (2.9553-3.5)/(0.5596/sqrt(17))
t = -4.0133
Get the critical value for df = N-1 = 16, one tail, alpha is 0.05:
-1.7459
Since our test statistic is much lower than the critical value, we reject the null hypothesis. There is enough evidence to conclude that games are shorter than 3.50 hours.
Chapt 11 # 58
The amount of income spent on housing is an important component of the cost of living. The total costs of housing for homeowners might include mortgage payments, property taxes, and utility costs (water, heat, electricity). An economist selected a sample of 20 homeowners in New England and then calculated these total housing costs as a percent of monthly income, five years ago and now. The information is reported below. Is it reasonable to conclude the percent is less now than five years ago?
Home Owner Five years ago Now
1 17% 10%
2 20 39
3 29 37
4 43 27
5 36 12
6 43 41
7 45 24
8 19 26
9 49 28
10 49 26
11 35% 32%
12 16 32
13 23 21
14 33 12
15 44 40
16 44 42
17 28 22
18 29 19
19 39 35
20 22 12
SOLUTION
Before After
1 17 10
2 20 39
3 29 37
4 43 27
5 36 12
6 43 41
7 45 24
8 19 26...

...Statistics 1
Business Statistics
LaSaundra H. – Lancaster
BUS 308 Statistics for Managers
Instructor Nicole Rodieck
3/2/2014
Statistics 2
When we hear about business statistics, when think about the decisions that a manager makes to help make his/her business successful. But do we really know what it takes to run a business on a statistical level? While some may think that businessstatistics is too much work because it entails a detailed decision making process that includes calculations, I feel that without educating yourself on the processes first you wouldn’t know how to imply statistics. This is a tool managers will need in order to run a successful business. In this paper I will review types of statistical elements like: Descriptive, Inferential, hypothesis development and testing and the evaluation of the results. Also I will discuss what I have learned from business statistics.
My description of Descriptive statistics is that they are the numerical elements that make up a data that can refer to an amount of a categorized description of an item such as the percentage that asks the question, “How many or how much does it take to “ and the outcome numerical amount. According to “Dr. Ashram’s Statistics site” “The quantities most commonly used to measure the dispersion of the values about...

...CLICK TO DOWNLOAD
BUS 308 STATISTICS FOR AMANAGERS
BUS 308 Week 1 DQ 1 Language
Numbers and measurements are the language of business.. Organizations look at results, expenses, quality levels, efficiencies, time, costs, etc. What measures does your department keep track of ? How are the measures collected, and how are they summarized/described? How are they used in making decisions? (Note: If you do not have a job where measures are available to you, ask someone you know for some examples or conduct outside research on an interest of yours.)
BUS 308 Week 1 DQ 2 Levels
Managers and professionals often pay more attention to the levels of their measures (means, sums, etc.) than to the variation in the data (the dispersion or the probability patterns/distributions that describe the data). For the measures you identified in Discussion 1, why must dispersion be considered to truly understand what the data is telling us about what we measure/track? How can we make decisions about outcomes and results if we do not understand the consistency (variation) of the data? Does looking at the variation in the data give us a different understanding of results?
BUS 308 Week 1 Problem Set Week One
Problem Set Week One. All statistical calculations will use the Employee Salary Data set (in Appendix section).
Using the Excel Analysis ToolPak function Descriptive Statistics, generate descriptive statistics for the salary data. Which variables...

...
Simply use statistics as a tool. You will be given a data. (Next year you will not be given data, you will gather data yoruself).
1. Data: one of the variables is dependent and other dependent. Can be multiple. Then do regression analysis. ANOVA for overall significance and Regression equation. And write based on ANOVA there is a significance or not.
2. Some comments on correlation: volume vs. horse power etc.
3. Hypothesis test of one population. I assume that the mean is etc etc. Small paragraph analysis below the results of the test. ANOVA for small, large and medium size businesses for example.
Simply use statistics as a tool. You will be given a data. (Next year you will not be given data, you will gather data yoruself).
1. Data: one of the variables is dependent and other dependent. Can be multiple. Then do regression analysis. ANOVA for overall significance and Regression equation. And write based on ANOVA there is a significance or not.
2. Some comments on correlation: volume vs. horse power etc.
3. Hypothesis test of one population. I assume that the mean is etc etc. Small paragraph analysis below the results of the test. ANOVA for small, large and medium size businesses for example.
Simply use statistics as a tool. You will be given a data. (Next year you will not be given data, you will gather data yoruself).
1. Data: one of the variables is dependent and other dependent. Can be...