51-101
Help!
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| If a value k is added to every element in a data set, how does this affect measures of center (mean, median, mode)? | +/- k to measures of center
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| If a value k is multiplied to every element in a data set, how does this affect measures of center (mean, median, mode)? | multiply/divide k to measures of center
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| If a value k is added to every element in a data set, how does this affect measures of spread (range, IQR, standard deviation)? | no change to measures of spread
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| If a value k is multiplied to every element in a data set, how does this affect measures of spread (range, IQR, standard deviation)? | multiply/divide k to measures of spread
variance: multiply/divide k^2
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| What is the Central Limit Theorem? | ensures sampling distribution will be approximately normal despite the population distribution
as sample size increases: shape becomes more normal, spread is smaller, and t* approaches z*
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| What is the Law of Large Numbers? | if we observe more repetitions of any chance process, the proportion of times a specific outcome occurs approaches a single value (true mean)
as the number of samples increases, the center approaches the true mean
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| What is the Empirical Rule? When does this apply? | 68% of data falls within 1 std, 95% of data falls within 2 std , and 99.7% of data falls within 3 std
only applies if data is normally distributed and z-scores are clean numbers (-3,-2,-1,0,1,2,3)
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| How does the mean and median compare in a graph that is symmetric? Skewed right? Skewed left? | symmetric: mean and median in middle
skewed right: mean close to peak of curve but pulled right
median peak of curve
skewed left: mean close to peak but pulled left
median peak of curve
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| What is the difference between bivariate vs univariate data? | bivariate: 2 variables
univariate: 1 variable
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| How are univariates displayed? Bivariates? | univariates: displays that only use 1 category (histogram, bar graph, pie chart, dot plot, box plot, box and whisker)
bivariate: displays that use 2 categories (2 way table, venn diagram, xy graph)
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| What is the explanatory variable? Response variable? | explanatory response variable: cause, variable that can be manipulated to change the response variable, x
response variable: predicted response, variable affected by explanatory response variable, y
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| What is the LSRL? Define all variables. | y-hat = a+bx
y-hat is the predicted response variable
x is the explanatory variable definition
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| What is the meaning of "least squares"? | minimizes sum of residuals squared of all observations from the prediction line
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| What does the slope mean in the context of a problem? | For every x, y is predicted to increase/decrease by ???
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| What does the y-intercept mean in the context of a problem? | If x is 0, y is expected to be y-intercept
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| What is r called? What does it mean in the context of a problem? | There is a strong/mild/weak positive/negative linear relationship between x and y. This is the correlation coefficient.
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| What is r^2 called? What does it mean in the context of the problem? | ??? of the variability of y is due to x.
This is the coefficient of determination.
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| What happens to the value of r if you switch the x and y variables? | r does not change
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| What happens to the value of r if you add a constant value to each response value? | r does not change
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| What happens to the value of r if you multiply a constant value to each response value? | r does not change
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| What happens to the value of r if you change the unit of measure? | r does not change
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| What are the possible values of r? | r ranges from -1 to 1
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| If r=0.3, what does that indicate about the association of your data set? | There is a weak, positive linear relationship between x and y
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| If r=-0.9 what does that indicate about the association of your data set? | There is a strong, negative linear relationship between x and y
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| How does r differ from the slope of the LSRL? | r measures the strength of linear relationship
slope measures how much the y will change when x changes by 1
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| How do you extract LSRL from a computer printout? | using y-hat = a + bx
use 1st number under coef for a
use the 2nd number under coef for b
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| How do you find the t-score from a computer printout? | take the coeff of x and divide it by the standard deviation
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| How does an outlier/influential point affect r, r^2, and the slope of a line? | OUTLIER
r: artificially reduces
r^2: artificially reduces
slope: pulls toward outlier
INFLUENTIAL POINT
r: artificially inflates
r^2: artificially inflates
slope: pulls toward influential point
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| How can you determine if a line is a good fit for a set of data? | residual plot randomly distributed
r^2, higher the better
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| What is the formula that involved slope, correlation, and standard deviation? | b = r (sy/sx)
b: slope
r: correlation coefficient
sy and sx: standard deviation of y and x
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| What point is always on any LSRL? | (x bar, y bar)
x bar: mean of x
y bar: mean of y
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| What does resistant and non resistant mean? | resistant: outliers do not greatly affect value
median, mode, IQR, Q1, Q3
non resistant: outliers greatly affect value
mean, standard deviation, range, r, r^2
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| What is s on the Minitab printout? | root square mean error
standard deviation of residuals
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| What is a residual? | difference between observed and predicted value
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| What is a residual plot? | scatter plot of residuals compared to the regression line
assess how well a regression line fits the data
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| If a residual is positive, how does your model compare with the actual value? | predicted underestimates actual
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| If a residual is negative, how does your model compare with the actual value? | predicted overestimates actual
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| If an observed point is above LSRL, is the residual positive or negative? | positive
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| If an observed point is below LSRL, is the residual positive or negative? | negative
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| What is the sum of all residuals (of an LSRL)? | 0
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| What is the difference between interpolation and extrapolation? | interpolation: estimation of values between known data points
extrapolation: estimation of values beyond known data points
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| What is the difference between correlation and causation? | correlation: measure of strength and direction of relationship between 2 variables
causation: how one variable affects another
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| What are two other ways an association/correlation can occur? | common response
confounding response
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| What is a common response? | changes in x and y are caused by changes in a lurking variable
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| What is a confounding response? | possibility that change in x is causing change in y OR
change in lurking variable causes change in y
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| What is the difference between a parameter and statistic? | parameter: describes the whole population
statistic: describes a sample
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| What is the difference between bias and variability? | bias: center of sampling distribution does NOT equal true value of parameter, aiming
variability: spread of sampling distribution, consistency
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| What is the best way to minimize both bias and variability? | increase sample size
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