Ohio State: Stats 1430- Regression & Correlation Study for Final Exam

Your boss gives you the following regression equation. Selling price = $5,240 + $33.80 (Number of Square Feet). How do you interpret the slope for this equation? a. As selling price increases by $1, square feet increases by $33.80 b. As selling price increases by $1, square feet increases by 5,240. c. As square feet increase by 1, selling price increases by $33.80 d. As square feet increases by 1, selling price increases by $5,240.

c. As square feet increase by 1, selling price increases by $33.80

A researcher is trying to use January temperatures to predict latitude. This means January temperature is the X (independent) variable and latitude is the Y (dependent) variable. (t/f)

true

Correlation of a sample (r) will always be a number between ___ and ____

-1 and 1

Correlation of Rainfall and Corn = 0.608 a. 60% of the points lie exactly on the regression line b. All of these choices are correct c. There is a moderate linear relationship between rainfall and bushels

c. There is a moderate linear relationship between rainfall and bushels

(t/f) Suppose the correlation between two variables X and Y is .8. That means the correlation between Y and X is -.8.

false

(t/f) Suppose the correlation between yards rushing and yards passing is .6. That means the correlation between feet rushing and feet passing is .6 x 12 (since you multiply yards by 12 to convert to feet).

false

(t/f) Your boss gives you the following regression equation. X = square feet and Y = selling price Selling price = $5,240 + $33.80 (Number of Square Feet). Does it make sense to interpret the Y-intercept for this equation?

false

Suppose you have 4 data sets whose scatterplots all show possible linear relationships. The four data sets have correlations of -0.10, +0.25, -0.90, and +0.80, respectively. Which of the correlations shows the strongest linear relationship? a. -.90 b. -0.10 c. +0.80 d. +0.25

a. -0.90

Bob wants to use house size to predict house price in Columbus. He starts out by making ascatterplot of data from 100 homes randomly selected from the current Columbus market. so, On Bob's scatterplot, which variable makes the most sense to appear on the X axis?

House size: bc he is using house size to predict (x is independent variable)

When finding the correlation between two quantitative variables, you will get the sameanswer if you switch X and Y. Explain briefly.

If you look at the formula for r (formula sheet is in the Course Info section of Carmen),you see that r measures how X and Y move together (numerator) compared to how theymove separately (denominator). If you switch the X's and Y's around in the entireformula you get the same answer, by commutative property of multiplication

What does SSE stand for? a. Sum of Squares for Error b. Statistics of Squares for Error c. Square of Sums for Error d. Sum of Squares for Extrapolation

a. Sum of Squares for Error

Suppose the correlation between X =price of a gallon of gasoline and Y = price of a gallon of milk is r = .30 (yes/no): Should we go on and try to make predictions for milk prices using gasoline prices using a straight line?

no

Suppose: 1. all the points on a scatterplot lie perfectly on a straight line going uphill 2. the mean of X and the mean of Y are both 2 3 the standard deviations of X and Y are exactly the same. Can you find the equation of the best fitting line with this information? (Hint: Think of the '5 number' way of finding the best-fitting line.)

yes

A researcher is trying to predict the linear relationship between January revenue and yearly revenue for her company. The correlation turns out to be .60. How does she interpret this correlation? a. There is a moderate positive linear relationship between January revenue and yearly revenue. b. There is a very strong positive linear relationship between January revenue and yearly revenue. c. There is a weak positive linear relationship between January revenue and yearly revenue.

a. There is a moderate positive linear relationship between January revenue and yearly revenue.

Suppose the equation y = 3.45 - 2.58x represents a valid regression equation and X can be used to predict Y. From this information, we know that X and Y have _____________ correlation. a. a negative b. not enough info to tell c. a positive d. no

a. a negative as x value increases, y will become a larger negative number

Data was collected on amount of rainfall (inches) and amount of corn produced (bushels per acre) for a number of years in Kansas. The output is shown below. Assume the scatter plot looks good. What are the units of slope in this situation? a. bushels per inch b. bushels per acre c. inches per bushel d. slope has no units

a. bushels per inch

Correlation is affected by _________.

outliers

Correlation is affected by outliers. (t/f)

true

Correlation is a measure of the strength and direction of what type of relationship between two quantitative variables?

linear relationship

True/false: Having a correlation of positive 0.96, means that there is a 96% chance that a subject at age 4 will have a vocabulary size of 1500 words.

False

True/false: The correlation of positive 0.96, means that 96% of the subjects observed had a vocabulary size that was greater than their age.

False

Bob is interested in examining the relationship between the number of bedrooms in a home and its selling price. After downloading a valid data set from the internet, he calculates the correlation. The correlation value he calculates is only 0.05. What does Bob conclude? a. Bob continues his research because even though there is no linear relationship here, there could be a different relationship. b. Bob gives up on his research because r = .05 means there is no relationship of any kind between bedrooms and selling price.

a. Bob continues his research because even though there is no linear relationship here, there could be a different relationship.

The personnel department keeps records on all employees in a company. Here is the information they keep in one of their data files: - Employee identification number - Last name - First name - Middle initial - Department - Number of years with the company - Salary ($) - Education Level (high school, some college, or college degree) Age (years) Which of the following combinations of variables would be appropriate to examine with a scatterplot? a. age and salary b. salary and education level c. education level and age d. all choices are correct

a. age and salary

Scatterplots examine relationships between what type(s) of variables? a) Categorical b) Quantitative c) Both categorical and quantitative variables

b) Quantitative

What should the residual plot look like if the regression line fits the data well? a. points fall around the horizontal line Y = 0 b. all of these choices are correct c. no fan shapes d. random patterns

b. all of these choices are correct

If a residual is negative, then that data point lies _________________ the regression line. a. above b. below c. exactly on

b. below

Correlation has . a) The same units as the data b) No units

b. no units

Correlation of Rainfall and Corn = 0.60 a. 36% of the variability in Bushels per acre is due to Inches of Rainfall. b. None of these choices is correct. c. 60% of the variability in Bushels per acre is due to Inches of rainfall

a. 36% of the variability in Bushels per acre is due to Inches of Rainfall. R^2= 0.6*0.6 = 0.36 = 36%