Intro to Statistics

Vocabulary

100

A straight line that minimizes the sum of the residuals squares: 

a) slope 

b) y-intercept 

c) least-squares regression line

c

200

The predicted change in the dependent variable (i.e., y) as the independent variable (i.e., x) changes: 

a) y intercept 

b) slope 

c) residual

b

300

The predicted value when the independent variable takes a value of zero: 

a) slope 

b) x-intercept 

c) y-intercept

c

400

The difference between what the line of best fit predicts for a given value of x and what the data actually shows. 

a) correlation coefficient 

b) outlier 

c) residual

c

500

Individual points that substantially change the correlation or the regression line: 

a) influential observation 

b) outlier 

c) residual

a

Interpretations

100

(pokemon's predicted height) = 12 + 2(berries fed per day). 

Interpret the slope:

For every increase of one berry, there is an expected height gain of 2 pounds.

200

(pokemon's predicted height) = 12 + 2(berries fed per day). 

Interpret the y-intercept:

If a pokémon eats zero berries tall, its height would be 12 inches.

300

(pokemon's predicted height) = 12 + 2(berries fed per day).

R^2 = 88.2%. Interpret this in context of the problem:

88.2% of the variation in height can be accounted for by the least squares regression line of height on berries fed.

400

Name an independent and dependent variable that are positively correlated. 

500

(pokemon's predicted height) = 12 + 2(berries fed per day).

Find the predicted height if one eats 7 and a half berries.

12 + 2(90) = 202 inches

Theoretical Questions

100

If points are randomly scattered in a graph without any clear linear pattern, is the correlation likely to be zero, 1, or -1?

Zero

200

The coefficient of determination (r^2) for a plot of values is 0.88. Is the correlation of the regression line (r) smaller or larger than this value?

It could be either 0.938 or -0.938, so the answer is either larger or smaller. These values are derived from taking the square root of the coefficient of determination. A negative correlation is plausible because when squared, it too yields a positive value.

300

Name an independent and dependent variable with a correlation coefficient (r) of -0.8

400

A study has found a strong relationship between the number of cars one owns and his or her lifespan. The correlation is 0.88, and the coefficient of determination is 0.775. Is this sufficient evidence to conclude that owning more cars improves one's lifespan?

No, because association does not imply causation

500

Points on the residual plot for certain data are randomly scattered, showing no pattern whatsoever. Can the researcher still fit this data with a linear model?

Of course! In fact, points on a residual plot MUST be randomly scattered in order to fit data with a linear model