Chapter 10: Two quantitative variables Flashcards
what are the three main aspects we focus on for a scatterplot?
- strength (observes how closely an association follows a pattern)
- Form (this class focuses on linear forms)
- Direction ( whether the relationship is positive or negative
If there is not a linear relationship, does that mean there is no relationship?
NO, just because there is no linear relationship, does not mean there is no relationship at all. can be parabolic or something else
What does r measure?
it measures the strength of straight-line association between two variables
what does r always lie between?
-1 and 1
is the correlation between x and y the same as between y and x?
YES
What is a probabilistic model?
a model to which includes both a deterministic component and a random error component
What is beta_0?
the estimated y-intercept of the line.
- the predicted value of y when x=0
- only statistically meaningful when x can take values that are close to zero
What is beta_1?
It is the estimated slope of the line.
- the expected change in y for every 1-unit increase in x
What is the coefficient of determination?
Denoted by R^2
- the proportion of variation in. the observed values of the y variable that can be explained by the regression of y on x
Between which values does R^2 always lie?
0 and 1
What does a value of R^2 near 0 suggest?
not very useful in making predictions
What does a value of R^2 near 1 suggest?
suggests its pretty useful
What is the practical interpretation of the coefficient of determination?
about 100(R^2)% of the variation in y can be explained by the regression model using x to predict y
What is extrapolating?
using the regression line to make predictions outside the range of x values in your data set, because the linear relationship may not hold outside of that range
