Agresti chapter 3

Question 1

Regression line

Answer 1

Predicts the value for the response variable y as a straight-line function of the value x of the explanatory variable.

Question 2

Predicted value of y

Answer 2

y-hat

Question 3

Equation for regression (aka prediction equation) line

Answer 3

Y-hat = a + bx.
a denotes the Y-intercept
b denotes the slope.

Question 4

Residuals

Answer 4

Prediction error. The actual value y - the predicted value y-hat. Absolute value is the distance between the point in the plot and the regression line

Question 5

Residual sum of squares (RSS)

Answer 5

Sum(residual)^2 = sum (y - y-hat)^2.

The better the line, the smaller the residuals and the smaller the RSS. The line is called the least squares method

Question 6

Slope formula

Answer 6

Slope = b = r(Sy / Sx). X-bar is the mean of x, Y-bar the mean of y, Sx the SD of x and Sy the SD of y

Question 7

Y-intercept formula

Answer 7

Y-intercept = a = y-bar - b(x-bar)

Question 8

Influential observation

Answer 8

When the x value is relatively high or low compared to the rest of the data and lies far from the trend line

Question 9

Lurking variable

Answer 9

third variable that explains the correlation. Correlation does not imply causation. Different from confounding, which is associated both with the response variable and explanatory variable.