Title - People Measurements in IB Math Studies
Introduction
The task was to gather the conclusive data from both 1st and 6th period IB Math Studies classes in the terms of each student’s separate data in the areas of height (measured in inches), shoe size, and arm span, also in inches. Data

...LinearRegression 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...

...Chapter 13
LinearRegression and Correlation
True/False
1. If a scatter diagram shows very little scatter about a straight line drawn through the plots, it indicates a rather weak correlation.
Answer: False Difficulty: Easy Goal: 1
2. A scatter diagram is a chart that portrays the correlation between a dependent variable and an independent variable.
Answer: True Difficulty: Easy Goal: 1 AACSB: AS
3. An economist is interested in predicting the unemployment rate based on gross domestic product. Since the economist is interested in predicting unemployment, the independent variable is gross domestic product.
Answer: True Difficulty: Medium Goal: 1 AACSB: REF
4. There are two variables in correlation analysis referred to as the dependent and determination variables.
Answer: False Difficulty: Easy Goal: 1
5. Correlation analysis is a group of statistical techniques used to measure the strength of the relationship (correlation) between two variables.
Answer: True Difficulty: Easy Goal: 2 AACSB: AS
6. The purpose of correlation analysis is to find how strong the relationship is between two variables.
Answer: True Difficulty: Easy Goal: 2
7. Originated by Karl Pearson about 1900, the coefficient of correlation describes the strength of the relationship between two, interval or...

...
A. DETERMINE IF BLOOD FLOW CAN PREDICT ARTIRIAL OXYGEN.
1. Always start with scatter plot to see if the data is linear (i.e. if the relationship between y and x is linear). Next perform residual analysis and test for violation of assumptions. (Let y = arterial oxygen and x = blood flow).
twoway (scatter y x) (lfit y x)
regress y x
rvpplot x
2. Since regression diagnostics failed, we transform our data.
Ratio transformation was used to generate the dependent variable and reciprocal transformation was used to generate the independent variable.
3. Check if the model is adequate by checking the t-statistic, R2 and F-statistic.
F statistic reveals that the equation used to determine the relationship between the x and y is functional. Using the test statistic for the test of coefficients, it was revealed that the constant value in the equation is not significantly different from 0. Also, it was revealed that the transformed x, significantly explains the dependent variable. Also, it was revealed that the measure of proportion of variability explained by the fitted value is relatively high with 96.23%. This means that transformed data in blood flow explains 96.23% of the variation in the transformed data in arterial oxygen.
4. Check the normality of residuals and equal variances
predict r, resid
kdensity r, normal
pnorm tx
qnorm tx
rvpplot tx
Before we could perform the numerical test, we must...

.... The following sample observations were randomly selected.
X: 5 3 6 3 4 4 6 8
Y: 13 15 7 12 13 11 9 5
a. Determine the coefficient of correlation.
b. Determine the coefficient of determination.
c. Interpret the result.
. The following sample observations were randomly selected.
X: 5 3 6 3 4 4 6 8
Y: 13 15 7 12 13 11 9 5
a. Determine the coefficient of correlation.
b. Determine the coefficient of determination.
c. Interpret the result.
. The following sample observations were randomly selected.
X: 5 3 6 3 4 4 6 8
Y: 13 15 7 12 13 11 9 5
a. Determine the coefficient of correlation.
b. Determine the coefficient of determination.
c. Interpret the result.
X Y XY
5 13 65 25 169
3 15 45 9 225
6 7 42 36 49
3 12 36 9 144
4 13 52 16 169
4 11 44 16 121
6 9 54 36 81
8 5 40 64 25
39 85 378 211 983
a.
The 0.89 indicates a very strong negative relationship between X and Y.
b. The coefficient of determination is 0.7921, found by (0.89)2.
c. X accounts for 79 percent of the variation in Y.
2. Bi-lo Appliance Stores has outlets in several large metropolitan areas in New England. The general sales manager plans to air a commercial for a digital camera on selected local TV stations prior to a sale starting on Saturday and ending Sunday. She plans to get the information for Saturday-Sunday digital camera sales at the outlets and pair them with the number of times the advertisement was shown on the local...

...Linear -------------------------------------------------
Important
EXERCISE 27 SIMPLE LINEARREGRESSION
STATISTICAL TECHNIQUE IN REVIEW
Linearregression provides a means to estimate or predict the value of a dependent variable based on the value of one or more independent variables. The regression equation is a mathematical expression of a causal proposition emerging from a theoretical framework. The linkage between the theoretical statement and the equation is made prior to data collection and analysis. Linearregression is a statistical method of estimating the expected value of one variable, y, given the value of another variable, x. The term simple linearregression refers to the use of one independent variable, x, to predict one dependent variable, y.
The regression line is usually plotted on a graph, with the horizontal axis representing x (the independent or predictor variable) and the vertical axis representing the y (the dependent or predicted variable) (see Figure 27-1). The value represented by the letter a is referred to as the y intercept or the point where the regression line crosses or intercepts the y-axis. At this point on the regression line, x = 0. The value represented by the letter b is referred to as the slope, or the coefficient of x. The slope determines the...

...
Simple LinearRegression Model
1. The following data represent the number of flash drives sold per day at a local computer shop and their prices.
| Price (x) | Units Sold (y) |
| $34 | 3 |
| 36 | 4 |
| 32 | 6 |
| 35 | 5 |
| 30 | 9 |
| 38 | 2 |
| 40 | 1 |
| a. Develop as scatter diagram for these data. b. What does the scatter diagram indicate about the relationship between the two variables? c. Develop the estimatedregression equation and explain what the slope of the line indicates. d. Compute the coefficient of determination and comment on the strength of relationship between x and y. e. Compute the sample correlation coefficient between the price and the number of flash drives sold. f. Perform a t test and determine if the price and the number of flash drives sold are related. Let α = 0.01. g. Perform an F test and determine if the price and the number of flash drives sold are related. Let α = 0.01. |
ANS:
b. Negative linear relationship.
c. | = 29.7857 - 0.7286xThe slope indicates that as the price goes up by $1, the number of units sold goes down by 0.7286 units. |
d. | r 2 = .8556; 85.56% of the variability in y is explained by the linear relationship between x and y. |
e. | rxy = -0.92; negative strong relationship. |
f. t = -5.44 < -4.032 (df = 5); reject Ho, and conclude x and y are related.
g. | F = 29.642 > 16.26;...

...EXECUTIVE SUMMARY
The study is undertaken to study retailers behavior towards Aircel in selected region. The data is collected directly by visiting outlets through structured interview scheduled. The statistical tools used to analyze the data are: Co-relation analysis, Simple LinearRegression and Multiple LinearRegression. The software used to analyze the data is Windostat version 8.6, developed by Indostat services, is an advanced level statistical software for research and experimental data analysis.
The study is carried mainly in the areas like Lokthkunta, Lalbazar, Kharkhana, Old Alwal, Suraram, Medchal, Miyapur, Balanagar, Bollaram, Yapral, Anandbagh, Malkajgiri, ECIL areas in Hyderabad city.
1. INTRODUCTION
Telecommunication was one of the world powerful tool of development. It is one of the key changer for continuous growth and in areas of reducing poverty, employment development, gender equity, balanced regional development and special protection for vulnerable sections of the society. Indian telecommunication sector has undergone as a growth engine for the Indian economy in the last decade with the country experiencing huge growth in wireless sector. The penetration of internet and broadband has also improved.
Telecom sector is broadly divided into:
1. Fixed line telephony.
2. Mobile telephony.
a. Global System for Mobile Communications...

...LINEARREGRESSION MODELS W4315
HOMEWORK 2 ANSWERS February 15, 2010
Instructor: Frank Wood 1. (20 points) In the ﬁle ”problem1.txt”(accessible on professor’s website), there are 500 pairs of data, where the ﬁrst column is X and the second column is Y. The regression model is Y = β0 + β1 X + a. Draw 20 pairs of data randomly from this population of size 500. Use MATLAB to run a regression model speciﬁed as above and keep record of the estimations of both β0 and β1 . Do this 200 times. Thus you will have 200 estimates of β0 and β1 . For each parameter, plot a histogram of the estimations. b. The above 500 data are actually generated by the model Y = 3 + 1.5X + , where ∼ N (0, 22 ). What is the exact distribution of the estimates of β0 and β1 ? c. Superimpose the curve of the estimates’ density functions from part b. onto the two histograms respectively. Is the histogram a close approximation of the curve? Answer: First, read the data into Matlab. pr1=textread(’problem1.txt’); V1=pr1(1:250,1); V2=pr1(1:250,2); T1=pr1(251:500,1); T2=pr1(251:500,2); X=[V1;V2]; Y=[T1;T2]; Randomly draw 20 pairs of (X,Y) from the original data set, calculate the coeﬃcients b0 and b1 and repeat the process for 200 times b0=zeros(200,1); b1=zeros(200,1); i=0 for i=1:200 indx=randsample(500,20); x=X(indx); 1
y=Y(indx); avg x = mean(x); avg y = mean(y); sxx = sum((x − avg x).2 ); sxy = sum((x − avg x). ∗ (y − avg y)); b1(i) = sxy/sxx;...

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