AP Statistics U3 Note

3.1 Scatterplots and Correlation

新的词：
自变量 –> explanatory variables => help to explain
因变量 –> response variables => measures the outcome

Scatterplots

relationship, two quantitative variables, same individuals

• axis
• spots

怎么描述

• overall pattern
  • direction (positive association)
  • form (linear pattern, exponential, logarithmic)
  • strength (do not very much from the linear pattern)
• 偏离该 pattern 的情况 –> outliers

There is a strong positive relationship between duration and interval. There seems to be a linear pattern in the graph. The points do not very much from the linear pattern. There do not appear to have any outliers

3.2-p1 Correlation

The ==direction== and ==strength== of the linear relationship

Formula:

=> positive association

解释的数值 ()

There is a very strong positive association between A and B.

Correlation does not imply causation 不能代表因果

A strong correlation between two variables does not mean that one caused the other.

3.2-p2 Least-Squares Regression

Regression line => a line could used to predict y according to x 用于预测

: predicted value from the model

解释:

The value y increase/decrease byfor each additional increase in x

解释:

When x equals to 0 the value y.

Extrapolation

离回归线超远

Residual

Least-squares regression line

How to choose: let the sum of the squared residual as small as possible

一条数据组的拟合线, which let residual 平方和尽可能最小

Residual plot

how will the line describe the data

（在0附近）分布越均匀，说明数据越契合linear pattern

• should show no obvious pattern
• as close to 0 as possible

Standard deviation of the residuals

how far off the predictions are using the residuals 用 residuals 描述 predictions 偏移有多大

approximate size of “typical” or “average” predicted error

Coefficient of Determination 决定系数

多少百分比的 y 的变动是可以被 least-squares regression line 解释的，并告诉我们这条回归线的预测结果的效果如何

前置条件

要前置条件干什么：我们用SST和SSE来找到未被 least-squares regression line 解释的 y值 的变动

Formula:

<result>% of the variation in the <response variable> is accounted for by the regression line.

How to read output

Calculate the regression line (using mean and standard deviation)

✨✨✨Put it together

• Only linear pattern could be described by correlation and regression line
• Not resistant. It can be influenced by outliers
• Switching x and y will not affect the values of r.
• Correlation does not imply causation 不能代表因果