Stats without Tears

What is regression in the context of a data set of (x,y) points?

Regression is the process of finding the best equation to describe the relationship between the variables.

What are the names of the x variable and the y variable in regression analysis?

The x variable is called the explanatory variable (or independent variable) and the y variable is called the response variable (or dependent variable).

What command activates diagnostics on a TI-83/84 calculator?

Use the [DiagnosticOn] command.

What step should you take before performing a regression analysis?

Plot the points to determine if they seem to lie along a straight line.

What is the least squares regression line?

It is the line that minimizes the sum of the squares of the vertical distances of the points from the line.

How is the correlation coefficient (r) interpreted?

It ranges from -1 to +1, measuring the strength and direction of the linear association between two variables.

What does a correlation coefficient of r = 0.94 indicate?

There is a strong positive correlation between the two variables.

What do you need to do if the points in a scatterplot don’t seem to form a straight line?

Do not perform a linear regression; consider other types of regression.

When using the TI-83/84, which command pastes the linear regression command into the home screen?

Press [STAT] then [►] and select the appropriate linear regression command.

How do you interpret the y-intercept in a regression equation?

It indicates the predicted value of y when x is 0, though it may not always have practical meaning.

What is the coefficient of determination (R²)?

It measures the proportion of variance in the dependent variable that can be explained by the independent variable.

What must be true for the residuals in a well-fitted regression model?

They should be randomly scattered and not show any patterns.

What is an important reminder when interpreting correlation?

Correlation does not imply causation.

What is the general rule for determining a significant correlation using decision points?

If the absolute value of the correlation coefficient is greater than the critical number, there exists a significant correlation.

How can you verify that the residuals do not show a trend?

By plotting the residuals against the independent variable.

What does it indicate if a correlation is reported as r = -0.75?

There is a strong negative correlation between the two variables.

What does a high standard deviation in the residual plot indicate?

It indicates a larger amount of error in prediction.

How do you perform a regression analysis to find ŷ?

Use the regression equation from the analysis and substitute the x value into it.

What should you generally avoid when using regression equations?

Avoid extrapolating beyond the range of the data.

Fill in the blank: The likelihood of an event occurring is known as __________.

probability.

Fill in the blank: The sum of probabilities of all possible outcomes of an experiment must equal __________.

Fill in the blank: In a probability distribution, the __________ represents the value of a random variable.

outcome.

Fill in the blank: When two events are independent, the probability of both events occurring is the product of their __________.

individual probabilities.

Fill in the blank: The __________ of an event is the number of favorable outcomes divided by the total number of possible outcomes.

probability.

Fill in the blank: If you flip a fair coin, the probability of getting heads is __________.

0.5.

Fill in the blank: The __________ rule states that the probability of the union of two events equals the sum of their probabilities minus the probability of their intersection.

addition.

Fill in the blank: A sequence of outcomes is called a __________ when it is a specific configuration in probability.

sample space.

Fill in the blank: In a standard deck of cards, the probability of drawing an Ace is __________.

4/52 or 1/13.

Fill in the blank: The __________ gives the likelihood of different outcomes from an experiment, represented in a table or graph.

probability distribution.

What is probability?

Probability is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1.

What does a probability of 0 mean?

A probability of 0 indicates that the event will not occur.

What does a probability of 1 mean?

A probability of 1 indicates that the event is certain to occur.

What is a random experiment?

A random experiment is a process that leads to one of several possible outcomes.

What is an event in probability?

An event is a specific outcome or a set of outcomes from a random experiment.

What is the complement of an event?

The complement of an event is the set of all outcomes in the sample space that are not in the event.

How do you calculate the probability of an event?

Probability of an event = (Number of favorable outcomes) / (Total number of possible outcomes).

What is conditional probability?

Conditional probability is the probability of an event occurring given that another event has already occurred.

What is the difference between mutually exclusive and independent events?

Mutually exclusive events cannot occur at the same time, while independent events do not affect each other's occurrence.

What is a probability tree diagram?

A probability tree diagram is a graphical representation that helps to visualize the outcomes of a probability experiment.

What is a total probability?

Total probability refers to the sum of probabilities of all mutually exclusive outcomes in a sample space, which equals 1.

What is a discrete probability distribution?

A discrete probability distribution is a statistical distribution that summarizes the probabilities of a set of discrete outcomes.

What is a continuous probability distribution?

A continuous probability distribution describes the probabilities of the possible values of a continuous random variable.

What is the law of large numbers?

The law of large numbers states that as the number of trials increases, the relative frequencies of events will converge to their theoretical probabilities.

What does sampling error refer to?

Sampling error refers to the difference between the sample statistic and the actual population parameter due to randomness in choosing the sample.

What are independent events?

Independent events are those whose occurrence or non-occurrence does not influence the probability of the other occurring.

What does it mean if two events are mutually exclusive?

If two events are mutually exclusive, it means that they cannot occur at the same time.

How is the probability of a compound event calculated?

The probability of a compound event is calculated using the addition rule for mutually exclusive events or the multiplication rule for independent events.

What is the binomial probability formula?

The binomial probability formula calculates the probability of getting exactly k successes in n independent Bernoulli trials, given by P(X=k) = (n choose k)(p^k)(1-p)^(n-k).

What is the concept of expected value in probability?

The expected value is a measure of the central tendency of a probability distribution, calculated as the sum of all possible values, each multiplied by its probability.