9. Confidence interval for mean value of Y given x

10. Prediction interval for a randomly chosen value of Y given x

11. Coeff. of Correlation

12. Adjusted R2

13. Variance Inflation Factor

14. Beta Weights

15. Partial F Test

SSER - sum of squares of error of reduced model SSEF - sum of squares of error of full model r – no. of variables dropped from full model.

16. Outliers
Measure | Potential Outliers |
Standardized residual, Studentized residual | > 3 (3 sigma level) | Mahalanobis distance | > Critical chi-square value with df = number of explanatory variables(Outliers in independent variable) | Cook’s distance | > 1 implies potential outlier |

Leverage values | > 2(k+1)/n, then the point is influential (k is the number of independent variables and n is the sample size) | SDFBeta | > 2/n |
SDFFit | |
17. Mahalanobis Distance
Mi = (Xi – X)2/ Sx
18. Cook’s Distance
Di =
∑j (Yj – Yj(i))2/k x MSE
19. Durbin Watson Test
Durbin Watson value close to 2 implies no auto-correlation
Durbin Watson value close to 0 implies positive auto-correlation Durbin Watson value close to 4 implies negative auto-correlation 20. Relationship between F and R2
F = (R2/1- R2) x ((n-(k+1))/k)
FORECASTING
1. Exponential Smoothing

2. Double Exponential Smoothing

3. Theil’s Coeff

U1 is bounded between 0 and 1, with values closer to zero indicating greater accuracy. If U2 = 1, there is no difference between naïve forecast and the forecasting technique If U2 < 1, the technique is better than naïve forecast

...means-independent sample t-test, define groups * H0: RateMen=RateWoman (do not differ) * Ha: Ratemen≠RateWoman (RateMen differs from RateWoman) * H0: u1 = u2 vs. HA: u1 ≠ u2 (this is two tailed ) also possible: * H0:uWomen≥ uMen vs. HA: uWomen0 OR d 6000 → Ha: p > 0,5 of Ha≠0,5 indien dubbelzijdig wilt testen.notice: one-sided testing!! |
15.4.2 The Multiple Regression Model 13- First compute the new variable Price Difference: Transform, Compute Variable - In the compute variable box edit PriceDif as Target Variable; edit in the Numeric Expression using the variable names from the variable list: IndPrice – Price; click on OK. - In the same way you let SPSS compute the target variable SqAdvExp with the numerical Expression: AdvExp ** 2. - In the Data View you see two new variables are created: PriceDif and SqAdvExp.- Now you can use the multiple linear regression as explained in appendix 14.4.1: Analyse / Regression / Linear with dependent variable Demand and independent variables: PriceDif, AdvExp and SqAdvExp | 18.4.2 The Wilcoxon Rank Sum Test and Mann-Witney U non-parametric version of a paired samples t-test- Analyse, Nonparametric...

...Helpful Advising Information
College of Sciences
October 16, 2012
I. General Education Requirements
A. “C” or better in ENGL 1158 (1159 for Honors students); “D” ok in ENGL 1157.
B. Literature can be any language; writing courses do not count.
C. Social Sciences – 6 hours, including 3 hours at 2000+ level.
1. Includes Anthropology, Economics, Geography, Political Science, Psychology,
Sociology, and Urban Studies.
2. History is NOT Social Science; it is Humanities.
D. Humanities – Film, Theater, and Communication Arts, English, Foreign Languages, History,
Philosophy, and Women’s and Gender Studies.
*A&S courses count as Humanities or Social Sciences.
E. Arts – Fine Arts, Music, and theater/dance/film-related courses in Film, Theater, and
Communication Arts.
* FTCA 2650 Oral Communications is NOT Arts.
Note: Mixing requirements from different catalogs is not permitted. The requirements of the selected catalog (any catalog in force during the student’s continuous enrollment) must be followed throughout the degree program. A student who breaks enrollment (either voluntarily or by compulsion) for two consecutive semesters (not one semester and a summer term) may not elect a catalog earlier than the one in force at the time of re-enrollment.
II. College of Sciences Requirements
A. Science courses that cannot be used for degree credit – see attachment 1.
B. Free elective restrictions – see attachment 2.
III. Transfer...

...Homework 2
Solution Key
Problem 1. Suppose that you sell short 500 shares of Intel, currently selling for $40 per share,
and you give your broker $15,000 to establish your margin account. Assume Intel pays no
dividends.
a) If you earn no interest on the funds in your margin account, what will be your rate of
return after one year if Intel stock is selling at (i) $44; (ii) $40; (iii) $36?
The gain or loss on the short position is 500 P . Invested funds are $15,000.
Therefore, your rate of return will be 500 P / 15000 . The returns in each of the
three scenarios are:
(i)
(ii)
(iii)
500 4 / 15000 13.3%
500 0 / 15000 0%
500 (4) / 15000 13.3%
b) If the maintenance margin is 25%, how high can Intel’s price rise before you get a margin
call?
Total assets in the margin account are $20,000 from the sale of the stock plus $15,000,
which was the initial margin. Your liabilities are 500P. A margin call will be issued when
35000 500 P
.25
500 P
P 56
Problem 2: You’ve borrowed $20,000 on margin to buy shares in Disney, which is now
selling at $40 per share. Your account starts at the initial margin requirement of 50%. The
maintenance margin is 35%. Two days later, the stock price falls to $35 per share.
a) Will you receive a margin call?
You will not receive a margin call. You borrowed $20,000 and with another $20,000 of
your own equity you bought 1000 shares of Disney at $40 a share. At $35 a share the...

...StatisticsFormulaSheet
Numerical Descriptive Measures
1. Population Variance = σ 2. Sample Variance = s
2 =
2
=
∑iN 1 ( x i − μ ) =
2
N n ( x − x) 2 ∑i =1 i
n −1
3. Inter‐quartile Range = Q 3 − Q1
Expectation and variance 1. Expected value of X: μ = E ( X ) = ∑ xp ( x )
2. Variance of X: σ
2 2 = ∑ ( x − μ ) p( x)
Probability 1. Additive Rule: P ( A ∪ B ) = P ( A) + P ( B ) − P ( A ∩ B ) 2. Multiplicative Rule: P ( A ∩ B ) = P ( A) P ( B ) , if A and B are independent
3. Complement Rule: P ( A) = 1 − P ( A)
Conditional Probability
1. Definition: P ( A | B ) =
P( A ∩ B) P( B)
2. Multiplicative Rule: P ( A ∩ B ) = P ( A) P ( B | A) = P ( B ) P ( A | B )
Binomial Distribution X ~ B(n, p)
1. P ( X = k ) = ⎜ ⎟ p (1 − p ) 2. E(X) = np; V(X) = np(1−p)
⎛n⎞ ⎝k⎠
k
n−k
=
n! k ! ( n − k )!
k n−k p (1 − p )
Normal Distribution X~ N(μ, σ)
1. Standard normal: Z =
X −μ
σ
Confidence Interval 1. z‐confidence interval:
2. t‐confidence interval: 3. Confidence interval for proportion:
x ± zα / 2
x ± t α / 2 , df
σ
n
s ( df = n − 1)
∧ p ± zα / 2
n ∧ ∧ p (1 − p )
n
1
Sample size
sample size to estimate the parameter μ to within B units with (1‐α)100% confidence: n =
⎡ zα / 2σ ⎤ ⎢ B ⎥ ⎣ ⎦ X −μ σ n
2
...

...Statistics
ANOVA & Least Squares
Tyrone Sewell
Statistics, MAT 201, Module V-CA5
Alfred Basta
December 20, 2009
Statistics
ANOVA & Least Squares
Look at the data below for the income levels and prices paid for cars for ten people:
| Annual Income Level |Amount Spent on Car |
|38,000 |12,000 |
|40,000 |16,000 |
|117,000 |41,000 |
|17,000 |3,500 |
|23,000 |6,500 |
|79,000 |21,000 |
|33,000 |5,000 |
|66,000 |8,000 |
|15,000 |1,500 |
|52,000 |6,000 |
Answer the following questions:
A. What kind of correlation do you expect to find between annual income and amount spent on car? Will it be positive or negative? Will it be a strong relationship? Base your answer on your personal guess as well as by looking through the data.
The annual income and amount of money spent on a car correlates that generally the greater the sum of income the larger portion of money spent on a car. The middle/low to middle income in datas spent the most with percentages ranging from the low 21% to 40%. The middle/high income percentages took a much smaller percentage rate...

...Linear Regression deals with the numerical measures to express the relationship between two variables. Relationships between variables can either be strong or weak or even direct or inverse. A few examples may be the amount McDonald’s spends on advertising per month and the amount of total sales in a month. Additionally the amount of study time one puts toward this statistics in comparison to the grades they receive may be analyzed using theregression method. The formal definition of Regression Analysis is the equation that allows one to estimate the value of one variable based on the value of another.
Key objectives in performing a regression analysis include estimating the dependent variable Y based on a selected value of the independent variable X. To explain, Nike could possibly measurer how much they spend on celebrity endorsements and the affect it has on sales in a month. When measuring, the amount spent celebrity endorsements would be the independent X variable. Without the X variable, Y would be impossible to estimate. The general from of the regression equation is Y hat "=a + bX" where Y hat is the estimated value of the estimated value of the Y variable for a selected X value. a represents the Y-Intercept, therefore, it is the estimated value of Y when X=0. Furthermore, b is the slope of the line or the average change in Y hat for each change of one unit in the independent...

...interquartile range (IQR) would be 6 - 4 = 2.
When the data set is large, the two definitions usually produce the same (or very close) results. However, when the data set is small, the definitions can produce different results.
The Variance
In a population, variance is the average squared deviation from the population mean, as defined by the following formula:
σ2 = Σ ( Xi - μ )2 / N
where σ2 is the population variance, μ is the population mean, Xi is the ith element from the population, and N is the number of elements in the population.
Observations from a simple random sample can be used to estimate the variance of a population. For this purpose, sample variance is defined by slightly different formula, and uses a slightly different notation:
s2 = Σ ( xi - x )2 / ( n - 1 )
where s2 is the sample variance, x is the sample mean, xi is the ith element from the sample, and n is the number of elements in the sample. Using this formula, the sample variance can be considered an unbiased estimate of the true population variance. Therefore, if you need to estimate an unknown population variance, based on data from a simple random sample, this is the formula to use.
The Standard Deviation
The standard deviation is the square root of the variance. Thus, the standard deviation of a population is:
σ = sqrt [ σ2 ] = sqrt [ Σ ( Xi - μ )2 / N ]
where σ is the population standard deviation, σ2 is the population variance, μ is the...