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AP STATS CHAPTER 3 TEST
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Terms in this set (26)
Explanatory v. response
test grade v. number of hours spent studying
the number of hours spent studying EXPLAINS the test score (the RESPONSE) you achieve
Explanatory Variable
(x) explains or influences changes in another variable
Response Variable
(y) measures the outcome of a study. You should always be predicting the response variable 'y'
Extrapolation***
the use of a regression line to make a predict 'y' for a value 'x' that is far OUTSIDE the range of the original x values
DANGER!!!
-the LSRL is only valid (and reliable) for values of x that are inside of the range of the original x-values, or perhaps just outside of that range.
Slope
The amount by which y is predicted to change when x increases by one unit
When describing a scatterplot, think "____"...
D irection: positive or negative
O utliers: are there any?
F orm: linear or curved?
S trength: very strong- strong-moderately strong-moderately weak-weak-very weak
Strength
the strength of a relationship in a scatterplot is determined by how closely the point follows a clear form. Strength can be de
Outlier
an individual value that falls outside the overall pattern of the relationship
If an outlier is influential: removing the point would markedly change the LSRL.
1.) points that are outliers in the y direction but not the x direction of a scatterplot have large residuals. Other outliers may not have large residuals. (usually not influential)
2.) Outliers in the x-direction that follow the overall pattern of the rest of the points are NOT influential.
3.) Outliers in the x direction that do NOT follow the overall pattern are often influential for the least-squares regression line.
Correlation
value ( r ) that measure the strength of the linear relationship between two quantitative variables
Basic Properties of correlation:
- switching x and y does not change r
-changing units of either/both variables does not change r
- r has NO UNITS!!!!!!!!!
-Correlation requires that both variables be quantitative
-Correlation only measures the strength of a LINEAR relationship between two variables
-a value of 'r' close to -1 or 1 does NOT GUARANTEE a linear relationship. Always plot your data........
Interpreting correlation
Correlation r measures both strength and direction of a linear relationship. > mention these when describing
-if 'r' is close to -1 or 1, it is STRONG.
-if 'r' is close to 0, it is WEAK
-if 'r' is positive, then the association is positive (as x increases, y increases)
-if 'r' is negative, then then the association is negative (as 'x' increases, 'y' decreases)
A positive association
is defined when the above average values of the explanatory are accompanied by above average values of the response
A negative association
is defined when the above average values of one variable are accompanied by below average values of the other
predicted value
y-hat} the value of the y variable for a given x variable
Direction
the direction of the scatterplot is usually linear or nonlinear
Residual
the difference between an observed value of the response and the value predicted
Actual y - Predicted y <- think, 'AP'
Be sure to include both the sign and the size of residual in your interpretation- and context, of course!
ex;
residual: -2.015 inches
In this year, the actual date of first bloom occurred about 2 days earlier than predicted based on the average March temperature.
ASSOCIATION DOES NOT IMPLY CAUSATION
a strong association is not enough to draw conclusions about CAUSE AND EFFECT between the variables. X does not always cause changes in Y.
***
Least squares regression line
watch vid.
(Also known as the line of best fit), the LSRL minimizes the sum of the squared residuals; i.e. the smallest possible sum of the squared residuals will occur if the linear model is the LSRL.
Finding the equation of a LSRL
1
Determining how well the LSRL models the relationship between two variables...
r^2 (the coefficient of determination) gives the proportion of the variation in y that can be explained by the linear relationship between x and y
s (the standard deviation of the residuals) gives the typical prediction error when the LSRL is used to predict y based on a given value of x.
be sure to interpret in CONTEXT
HOW ARE EACH OF THE FOLLOWING INFLUENCED BY OUTLIERS?
1. Slope of LSRL
2. y-intercept of LSRL
3. s
4. r^2
q
A regression line
a line that describes the relationship between two quantitative variables
Scatterplot
a graphical display of the relationship between two quantitative variables
The coefficient of determination
r^2 describes the fraction of variability in y values that is explained by least squares regression on x
Influential points
individual points that substantially change the correlation or slope of the regression line
Making & Interpreting a Residual Plot *****
Residual Plot: scatterplot of x and residual (list of residuals computed by hand or using calculator)
x vs. residual
-if there is no obvious pattern in the residual plot, then the linear model is appropriate
-if there is an obvious pattern (e.g. a curve) in the residual plot then the linear model is NOT appropriate
CALCULATOR CHECK: CAN YOU....
-enter lists (and clear them when you are ready to enter new lists)
-make a scatterplot (x v. y)
-find the correlation 'r' between x and y
-find the equation of the LSRL (and graph it with the scatterplot)
- make a residual plot (x vs. residual)
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