Least-Squares Regression and Corr. Coefficient
In a least-squares regression line, x can be thought of as the __________ variable.
What is explanatory/predictory ?
Name two conditions for a random variable to be considered a binomial distribution.
Answers can include:
1. Fixed number of trials.
2. Only two possible outcomes for each trial.
3. Trials are independent.
4. Probability of success is the same for each trial.
5. X represents number of successes that occur.
In an approximately normal distribution, what percentage of data lies within 1 standard deviation?
What is 68%?
The mean of a discrete probability distribution is also known as what?
The expected value.
In an approximately normal distribution, what percentage of data lies within 2 standard deviations?
What is 95% ?
If the correlation coefficient of two variables is -.891, what does this indicate about their relationship?
I'm looking for two things!
They have a strong relationship. They are also negatively correlated, so as one variable increases the other variable decreases.
Before marketing a new product on a large scale, many companies conduct a consumer- preference survey to determine whether the product is likely to be successful Suppose a company develops a new diet soda and then conducts a taste- preference survey in which 100 randomly chosen customers state their preferences among the new soda and the two leading sellers. Let x be the number of the 100 who choose the new brand over the two others.
Is this a binomial experiment?
Yes.
In a probability density curve, the probability that x equals a single point or value is _____ and the total area under the curve is _____
What is 0;1
Find the missing value.
x 0 1 2 3 4
P(x) .15 .08 .34 .21
What is .22?
Give an example of qualitative data and an example of quantitative data.
Qualitative: eye color
Quantitative: distance
A correlation coefficient can only be used to measure the strength of what type of relationship?
What is linear?
Provide the definitions for n, p, and 1-p in a binomial experiment.
n= number of trials
p= probability of success
1-p= probability of failure
What are the two interpretations of the area between two points in a probability density curve?
2. It represents the proportion of the population whose values are between those two points.
What is a random variable?
A numerical outcome of a probability experiment.
Q3-Q1 is known as what?
What is the interquartile range?
Consider this least-squares regression line for predicting the weight of a football player from his height:
y=1.588x+107.27
If two quarterbacks differ in height by two inches, by how much would you predict their weights to differ?
3.176 pounds.
The Centers for Disease Control and Prevention reports that 25% of baby boys 6-8 months old in the US weigh more than 20 pounds. A sample of 16 babies is studied.
What is the mean number of babies who weigh more than 20 pounds in a sample of 16 babies aged 6-8 months?
What is 4?
A normal distribution with a mean of 0 and a standard deviation of 1 is called a _______________________.
What is a standard normal distribution?
Explain the law of large numbers.
For a large sample, the sample mean will almost certainly be close to the population mean.
What is a systematic sample?
A type of probability sampling method in which sample members from a larger population are selected according to a random starting point and a fixed, periodic interval.
Compute the least-squares regression line given the following values:
x̄= 45000 sx= 20000 r= .40
ȳ= 100 sy= 15
What is y=.0003x + 86.5?
According to a report of the Nielsen Company, 67% of Internet searches in July 2013 used the Google search engine. Assume that a sample of 25 searches is studied.
What is the probability that 15 or fewer used Google?
What is .2919?
Former ISU basketball player Kelvin Cato is 83 inches tall. Assuming that heights follow approximately a normal distribution with mean 70 and standard deviation σ = 3, find the proportion of men that are shorter than him. Also, calculate his z-score and interpret it.
Z-score is 4.33. This means that Kelvin Cato's height is very unusual.
Find the expected value of the following discrete probability distribution.
x 1 2 5 7
P(x) .42 .18 .34 .06
What is 2.9?
What is the difference between the empirical rule and Chebyshev's Inequality?
Answer can include:
1. Empirical rule can only be used for bell-shaped histograms while Chebyshev's Inequality can be used for any histogram.
2. Empirical provides us with exact percentages while Chebyshev's Inequality only provides us with minimum percentages.