Stock and Watson Chapter 5: Regression with a Single Regressor what do the distributions of 1 and 0 look like? if the sample is sufficiently large (n=100), then: 1 ~ N (1 , standard deviation given by formula on page 133 SW, 587 MM) ~ N (0, standard devia
Stock and Watson Chapter 4: Linear Regression with One Regressor The linear regression model is: Yi = 0 + 1Xi + ui The subscript i runs over observations, i= 1,n; Yi is the dependent variable (or the regressand or the response variable or the left-hand-si
Stock and Watson Chapter 2.3- Two Random Variables Joint distribution The joint probability distribution of two discrete random variables, say X and Y, is the probability that the random variables simultaneously take on certain values, say x and y. The pr
Section Problems #3 #1) Student Student 1 Student 2 Student 3 IQ score 110 124 126 Self-concept score 58 72 83
a) What is the standard deviation of IQ scores? Round your answer to four decimal places. (2 points) b) What is the standard deviation of self-c
Section Problems #3 #1) Student Student 1 Student 2 Student 3 IQ score 110 124 126 Self-concept score 58 72 83
a) What is the standard deviation of IQ scores? Round your answer to four decimal places. (2 points) b) What is the standard deviation of self-c
Section Problems #2 From book: 1.136 (page 75) Express your answers as proportions instead of percents. Round your final answers to four decimal places. 1.139 (page 75) Express your answers as proportions instead of percents. Round your final answers to f
Section Problems #1 Circle all of your final answers. #1) Conservationists have despaired over destruction of tropical rainforest by logging, clearing, and burning. These words begin a report on a statistical study of the effects of logging in Borneo. Res
1 Rounding on problem sets and exams Rounding is an issue in this class. As a rule of thumb, if the question doesn't specify and you need to round your final answer, you should round it to four decimal places. Always use the common method of rounding. htt
Statement on the Grading of Exams On the exams, I am testing your ability to actually correctly solve the problems. The point of statistics is to arrive at the correct final answer. For example, if you are working as a research assistant and you are asked
Completing Blackboard Problem Sets The Blackboard problem sets will be posted under Assignments. Click on the problem set and it will open up. You should then print out the problem set. You can exit Blackboard. Solve the problems and write down the answer
6.2
Tests of Significance
Example #1 borrowers at private 4-year college: mean debt ( a )= $21,200 (survey result) borrowers at public 4-year college: mean debt ( b )= $17,100 (survey result) the difference $4100 ( a - b ) is fairly large/ but these numbe
4.4
Means and Variances of Random Variables Mean of a discrete random variable
Suppose that X is a discrete random variable whose distribution is Value of X Probability x1 x2 x3 xk p1 p2 p3 pk
To find the mean of X, multiply each possible value by its pro
4.2
Probability Models
probability model- a description of a random phenomenon in the language of mathematics the description of a random variable has two components: a list of possible outcomes a probability for each outcome The sample space S of a rando
4.1
Randomness
toss a coin- cant predict result in advance (results vary) a regular pattern emerges after many repetitions We call a phenomenon random if individual outcomes are uncertain but there is nonetheless a regular distribution of outcomes in a la
3.3 Toward Statistical Inference Statistical inference is using a fact about a sample to estimate the truth about the whole population. A simple random sample (SRS) of size n consists of n individuals from the population chosen in such a way that every se
3.2 Sampling Design population- the entire group of individuals we want information about sample- the part of the population that we actually examine in order to gather information sample survey- survey a sample to gain info about the population voluntary
3.1
Design of Experiments
experimental units- individuals on which the experiment is done subjects- experimental subjects that are humans treatment- specific experimental condition applied to the units factors- explanatory variables in experiment levels-
2.6 The Question of Causation Often the goal in a study is to establish that changes in the explanatory variable cause changes in the response variable. What constitutes good evidence of causation? What different types of links between x and y can explain
2.4
Cautions about Correlation and Regression
regression- after fit a line to data, can see scatter of data points about regression line regression makes sum of squares of vertical distances from the data points and the regression line are as small as pos
2.3
Least-Squares Regression (OLS)
correlation measures the direction and strength of the linear relationship between two quantitative variables we would like to summarize the overall pattern by drawing a line on the scatterplot A regression line is a str
2.2
Correlation
scatterplots display the relationship between two variables linear (straight-line) relationships are important because they are quite common linear relationship is strong if points lie close to a straight line linear relationship is weak i
Chapter 2- Looking at Data we often care about the relationship between two variables to study the relationship, we measure both variables on the same individuals Two variables measured on the same individuals are associated if some values of one variable
Normal Quantile Plots Normal quantile plots are used to determine whether or not data distributions are normal. Constructing a normal quantile plot 1. Arrange the observed data values from smallest to largest. Record what percentile of the data each value
1.3 Density Curves and Normal Distributions
Density Curve idealized description of data distribution smooth approximation to the irregular bars of a histogram Density Curve The curve is always on or above the horizontal axis. The curve has area exactly 1
9.1 Inference for Two-Way Tables exclusive territory- new store will be the only representative of the franchise in a specified territory and will not have to compete with other outlets of the same chain Effect of having an exclusive territory on the succ
8.1 recall from 5.1, when n is large:
Inference for a Single Proportion p ~ N (p, p (1 p ) ) n
Large-sample confidence interval for a population proportion Choose an SRS of size n from a large population with unknown proportion p of successes. The sample
7.2
Comparing Two Means
two-sample problems are among the most commonly encountered in statistics compare control group and treatment group Two-sample problems the goal of inference is to compare the responses in two groups each group is considered to be
7.1
Inference for the Mean of a Population
the sampling distribution of x depends on when is unknown, we must estimate even though we are primarily interested in the sample standard deviation (s) is used to estimate the population standard deviation ()
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