week 4 carmen quiz: correlation and regression

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. How do you interpret the correlation here? Predictor Coef SE Coef T P Constant 89.543 6.703 13.36 0.000 Rainfall 0.12800 0.01375 9.31 0.000 Correlation of Rainfall and Corn = 0.608

There is a moderate linear relationship between rainfall and bushels

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?

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

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?

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

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?

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

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 is the equation of the regression line? Predictor Coef SE Coef T P Constant 89.543 6.703 13.36 0.000 Rainfall 0.12800 0.01375 9.31 0.000 Correlation of Rainfall and Corn = 0.608 (see pic)

Bushels per acre = 89.543+.128 x inches of rain

Suppose the correlation between X =price of a gallon of gasoline and Y = price of a gallon of milk is r = .30 Should we go on and try to make predictions for milk prices using gasoline prices using a straight line?

false

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 the correlation between two variables X and Y is .8. That means the correlation between Y and X is -.8.

false

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

What should the residual plot look like if the regression line fits the data well?

no fan shapes points fall around the horizontal line Y = 0 random patterns all choices are correct!

correlation is affected by outliers

true

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

What does SSE stand for?

Sum of Squares for Error

If a residual is negative, then that data point lies _________________ the regression line.

below

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?

-0.90

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. Which of the following statements is true? Predictor Coef SE Coef T P Constant 89.543 6.703 13.36 0.000 Rainfall 0.12800 0.01375 9.31 0.000 Correlation of Rainfall and Corn = 0.60

36% of the variability in Bushels per acre is due to Inches of Rainfall.

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.

negative

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?

age and salary

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? predictor Coef SE Coef T P Constant 89.543 6.703 13.36 0.000 Rainfall 0.12800 0.01375 9.31 0.000 Correlation of Rainfall and Corn = 0.608 (see pic)

bushels per inch

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.

true