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Chapter 5 AP Statistics
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LSRL Residuals Correlation
Terms in this set (24)
X-variable
independent or explanatory variable
Y-variable
dependent or response variable
Y-hat
predicted y
B
slope; the amount by which the y increases when x increases by 1 unit
a
y intercept. It is the height of the line when x=0.
LSRL
least square regression line; line that gives the best fit to the data set; minimizes the sum of the squares of the deviations from the line
Slope interpretation statement
For each unit increase in x, there is an approximate increase/decrease of b in y.
Correlation coefficient interpretation statement
There is a direction, strength, type of association between x and y.
Extrapolation
Not knowing whether the pattern observed in the scatterplot continues outside the range.
Non resistant
affected by outliers
Correlation Coefficient (r)
a quantitative assessment of the stregnth and direction of the linear relationship between bivariate, quantitative data
Properties of (r) weak
0-.5
Properties of (r) moderate
.5-.8
Properties of (r) strong
.8-1
Value of r
a measure of the extent to which x & y are linearly related
Correlation does not imply causation
Correlation does not imply causation
Residuals
The verticle deviation between the observations & the LSRL
Sum of residuals
Always zero
Residual equation
residual=y-yhat
Residual plot
No pattern in residual plot then association is linear. Residual plots are the same no matter if plotted against x or y-hat
Coefficient of determination r^2
gives the proportion of variation in y that can be attributed to an approximate linear relationship between x and y. remains same no matter which variable labeled x
Interpretation statement of r^2/ coefficient of determination
Approximately r^2% of the variation in y can be explained by the LSRL of x & y
Outlier
a date point with a large residual
Influencial point
A point that influences where the LSRL is located. If removed, it will significantly change the slope of the LSRL
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