EXAM 3 FINAL

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    What is the purpose of using two columns of data values in linear relationships?

    To measure how the values of two variables move relative to each other.

    Do the two columns of data values in linear relationships have to be dependent?

    Independent data values can also be used.

    Why is it important to look at the scatterplot first in linear relationships?

    To check for extreme values and unusual patterns.

    Why couldn't statistics prove smoking caused lung cancer?

    A lurking variable could affect the results.

    What is the key purpose of a scatterplot in linear relationships?

    To see any relationship between two variables.

    Which variable is always plotted on the y-axis in linear relationships?

    The response variable.

    How are predictor and response variables determined in a dataset?

    The variable that changes first is the predictor.

    What is the key purpose of linear correlation?

    To summarize the linear component between two variables.

    What two characteristics does linear correlation measure?

    The strength and direction of the linear relationship.

    What is the key purpose of linear regression?

    To determine the effect of one variable on another.

    What is the theoretical objective of linear regression?

    To find the direction and strength of the linear relationship.

    What statistical method is used for linear regression in this book?

    The Least Squares method.

    Is a dataset with Height and Weight appropriate for measuring movement?

    Yes, because both variables can be measured from one individual.

    Can statistics show that higher tariffs imply higher prices?

    No, as statistics cannot determine causation.

    What characteristic of two columns of data values is measured?

    The movement between the data values.

    What is the consequence of using two columns of independent data values?

    The statistical results may lack meaning.

    What key points should be kept in mind when interpreting results?

    Correlation does not imply causation.

    Where does a lurking variable exist?

    Outside of the variables measured.

    Why is the presence of a potential lurking variable important?

    It can affect statistical results without being known.

    What does the movement between two variables mean in terms of data values?

    How one variable's variance changes with the other.

    What type of relationship can be seen in a scatterplot?

    Any linear relationship between the two variables.

    What type of relationship can be detected with correlation?

    Only a linear relationship.

    Can correlation measure a linear relationship?

    Yes, it measures the strength of the linear relationship.

    What are possible values for the linear correlation statistic?

    -1 to +1, including the endpoints.

    What additional information does linear regression provide over correlation?

    The size of the effect of the predictor variable.

    How is information about a linear relationship summarized in regression?

    By the equation of the line of best fit.

    What is the purpose of a scatterplot?

    To measure the linear relationship between two variables.

    What are the three types of overall patterns to look for in a scatterplot?

    Linear, curvilinear, and no relationship.

    What is the practical meaning of a positive/negative linear relationship?

    Data values move together or opposite.

    What are the three exceptions to look for in a scatterplot?

    Peaks, gaps, and extreme values.

    Why is knowing about extreme values important?

    They can skew statistical results.

    What is the purpose of linear correlation?

    To measure the linear component of data pairs.

    Why is knowing a linear relationship important in statistics?

    It provides a clear summary of variable relationships.

    What is the first step in calculating linear correlation?

    Standardize the raw data values into z-scores.

    What value of Pearson’s correlation coefficient indicates no linear relationship?

    r = 0.

    What part of the correlation coefficient indicates the direction of the relationship?

    The mathematical sign of the correlation coefficient.

    What part of the relationship does the correlation coefficient measure?

    Only the linear component of the relationship.

    How are extreme values seen in a scatterplot?

    As dots outside the overall pattern.

    What are the two steps to analyze a scatterplot?

    Look at the overall pattern and exceptions.

    What method is used to visually estimate the linear component in a scatterplot?

    The Rubber-Band method.

    What is the direction of the linear relationship in scatterplots?

    Variables move together or opposite.

    Which scatterplot shows a higher linear relationship?

    The one with points closer to a line.

    What overall pattern is shown in a scatterplot with extreme values?

    One linear relationship with extreme values.

    What is the relationship between two variables in scatterplots?

    One may show a linear relationship while the other does not.

    What are two reasons for using statistical methods over scatterplots?

    Mathematical methods quantify relationships.

    What calculations are the foundation for linear correlation?

    Multiplying z-scores and summing.

    How many positive and negative signs would you expect in a correlation table for a coefficient near zero?

    Nearly equal numbers of positive and negative signs.

    What two characteristics of a linear relationship are expressed in a correlation coefficient?

    Direction and strength.

    What are appropriate linear correlation coefficients for different plots?

    Values indicating the strength and direction of relationships.

    How does the Rubber Band method indicate a high linear component?

    By forming a long, narrow oval shape.

    Which scatterplot shows a lower linear correlation coefficient?

    The one with points farther from a straight line.

    How does an extreme value affect the linear correlation coefficient?

    It can skew the results significantly.

    What is the correlation coefficient between height in inches and weight in ounces if height in feet and weight in pounds is 0.40?

    Cannot be determined from the information given.

    Why is the middle point in a histogram important?

    It represents the balance point of data values.

    Why is the middle line of a scatterplot important?

    It helps find the relationship between two columns.

    Why is the equation of the middle line of a scatterplot important?

    It allows for explanation and prediction.

    What is the name of the middle line of a scatterplot?

    The regression line.

    What is the appropriate name for regression with one predictor and one response variable?

    A simple regression.

    What new information does linear regression provide over correlation?

    The size of the effect on the response variable.

    How are results given for linear regression?

    In the equation of the regression line.

    What is the equation for a linear regression line?

    y = mx + b.

    What are the correct symbols for the y-intercept and slope in a regression line?

    y-intercept = b0, slope = b1.

    What assumption about residuals in a linear regression line is true?

    They are normally distributed around the regression line.

    What is an example of using a regression line for explanation?

    If x goes up one unit, then y goes up by the slope.

    What is an example of using a regression line for prediction?

    If x equals a certain value, then predict y.

    What is the concept of a residual in simple linear regression?

    The vertical distance from the point to the regression line.

    What is the value of the residual for a point on the regression line?

    Residual = 0.

    In simple linear regression, how many predictor and response variables are there?

    One predictor and one response variable.

    What assumptions must be met for linear regression?

    Data values must be independent and normally distributed.

    What terms are needed to use a regression equation for prediction?

    Both the y-intercept and the slope.

    What is an important consequence of the Scope of the Model?

    Valid for interpolation inside the range of the predictor variable.

    Which point is closest to the regression line?

    The point with the smallest residual.

    How does linear regression find the equation of the regression line?

    By minimizing the sum of the squared residuals.

    What is the change in weight if height increases by one inch?

    Weight would go up by the slope value.

    What is the change in weight if height increases by one foot?

    Weight would go up by 12 times the slope.

    What is the change in weight if height decreases by six inches?

    Weight would go down by six times the slope.

    What is the change in weight if height increases by twelve inches?

    Weight would go up by twelve times the slope.

    What is the predicted price of a used car that is one year old?

    Calculate using the regression equation.

    What is the residual for a two-year-old car with an asking price?

    Calculate using the regression equation.

    What is the prediction for purchasing a five-year-old car?

    Compare to the predicted price from the regression.

    What is the predicted price of a 2.5 carat diamond?

    Calculate using the regression equation.

    Why is a negative price for a diamond not appropriate?

    Price cannot be negative in economic terms.

    How is a residual found in linear regression?

    The difference between the observed and predicted values.

    What is a residual in a histogram analogous to?

    A deviation.

    How is a residual calculated?

    Residual = observed value - predicted value.

    Why does the sum of all residuals equal zero?

    Positive and negative residuals cancel out.

    How does the least squares method find the regression line?

    By minimizing the sum of squared residuals.

    What does finding the regression line mean?

    Find the slope and y-intercept using least squares.

    What is the importance of a positive/negative slope?

    Indicates the direction of data movement.

    What is the critical value for a two-tail hypothesis test at 90% confidence?

    CV = ±1.64.

    What is the proper conclusion to a hypothesis test?

    Reject or do not reject the null hypothesis based on p-value.

    What does the phrase Normal Approximation to the Binomial mean?

    Using a normal curve to approximate a binomial histogram.

    What is the probability that more than 40 drivers were speeding?

    Calculate using binomial probability.

    What is the probability that at least 70 people don't floss enough?

    Calculate using binomial probability.

    What is the probability that less than 30 people don't have their dog vaccinated?

    Calculate using binomial probability.

    What is the probability that 30 or less people don't have their dog vaccinated?

    Calculate using binomial probability.

    What is the probability that less than 75 women wear red lipstick?

    Calculate using binomial probability.

    What is the probability that no more than 75 women wear red lipstick?

    Calculate using binomial probability.

    What is the statistical method for the relationship between two binomial variables?

    To determine if the two variables are independent.

    Can the Chi Square Test for Independence be used with continuous data?

    No, it can only be used with categorical data.

    What type of information does the Chi Square Test for Independence give?

    Probability information.

    Does the Chi Square Test for Independence result in a p-value?

    Yes, as it is a hypothesis test.

    What is the range and shape of Chi-Square curves?

    (0, ∞) / Skewed right.

    What is the fundamental concept of the Chi-Square test based upon?

    The deviation between observed and expected frequencies.

    What is the chi-square test of independence?

    A hypothesis test for two binomial variables.

    What is the statistical meaning of the null hypothesis in a chi-square test?

    The two variables are independent.

    What is the difference between a 2x2 table of descriptive statistics and a chi-square table?

    The chi-square table includes expected frequencies.

    What is a p-value in a chi-square test of independence?

    The tail area from the test statistic to positive infinity.

    Are attending class and passing an exam independent or dependent?

    Dependent, because the p-value is low.

    Are being overweight and eating fast food related?

    Related, because the p-value is low.