Predicting student proficiency test scores accounting for poverty and income measures: Data was collected on 608 school districts in Ohio (The Cincinnati Enquirer, Nov 30, 1997) using passage rates in 1996. The variables used in this analysis include: % passed – percent of all 4rth, 6th, 9th and 12th graders who passed the state’s exam eg.: 93.85 means 93.85% % on ADC – percent of all students in the district receiving Aid for Dependent Children eg.:0.11 means 0.11% % Free Lunch – percent of all students who qualify for reduced- priced lunches Median Income – reported in dollars 1. The following scatterplots in the attachments were constructed to observe the relationship between each of the potential independent variables to predict student success rates as measured by percent passed. What is the primary purpose of constructing these scatterplots? 2. Which variable appears to be the strongest predictor of passing rates? 3. What descriptive statistics would you calculate to measure the strength and direction of the relationship between the variable selected in question 2 and the Ohio passing rates?
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
Predicting student proficiency test scores accounting for poverty and income measures: Data was collected on 608 school districts in Ohio (The Cincinnati Enquirer, Nov 30, 1997) using passage rates in 1996. The variables used in this analysis include:
% passed – percent of all 4rth, 6th, 9th and 12th graders who passed the state’s exam
eg.: 93.85 means 93.85%
% on ADC – percent of all students in the district receiving Aid for Dependent Children
eg.:0.11 means 0.11%
% Free Lunch – percent of all students who qualify for reduced- priced lunches
1. The following scatterplots in the attachments were constructed to observe the relationship between each of the potential independent variables to predict student success rates as measured by percent passed. What is the primary purpose of constructing these scatterplots?
2. Which variable appears to be the strongest predictor of passing rates?
3. What
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