Question

Question 1

How is a residual calculated in a regression model? i.e. what is the meaning of a residual?

a)The difference between the actual value, y, and the fitted value, y-hat

b)The difference between the fitted value, y-hat, and the mean, y-bar

c)The difference between the actual value, y, and the mean, y-ba

d)The square of the difference between the fitted value, y-hat, and the mean, y-bar

Question 2

Larger values of r-squared imply that the observations are more closely grouped around the...

a)the origin of the plot (0,0)

b)average value of the outcome

c)best fit line

d)average value of the predictors

Question 3

What diagnostic plot shows us influential outliers?

a)Scale-Location

b)Residuals vs. Leverage

c)Residuals vs. Fitted

d)QQ Plot

Question 4

What is heteroscedasticity?

a)When our model violates the assumption of normal residuals

b)A violation of the assumption of constant variance

c)An important assumption of OLS regression that means our variables are all different

d)The important assumption that our errors are independent (i.i.d.)

Question 5

Regression analysis was applied to return rates of sparrowhawk colonies. Regression analysis was used to study the relationship between return rate (x: % of birds that return to the colony in a given year) and immigration rate (y: % of new adults that join the colony per year). The following regression equation was obtained.

Based on the above estimated regression equation, if the return rate were to decrease by 10% the rate
of immigration to the colony would:

a)decrease by 3.4%

b)increase by 34%

c)increase by 3.4%

d)decrease by 0.34%

Question 6

In regression analysis, if the independent (predictor) variable is measured in kilograms, the dependent (outcome) variable...

a)must be in some unit of weight

b)must also be in kilograms

c)can be any units

d)cannot be in kilograms

For this quiz we fill investigate a series of linear models fit using the dataframe, brainhead.

Description: Brain weight (grams) and head size (cubic cm) for 237
adults classified by gender and age group.

Variables/Columns
gender: 1=Male, 2=Female
agegroup: 1=20-46, 2=46+
size_cm3 - headsize in cubic centimeters (cm^3) 
weight_grms - weight of brain in grams

We will focus on predicting the "outcome" / DV brain weight (weight_grms) using the numeric variable head size (size_cm3).

The rest of the questions refer to the simple linear regression model (brainhead model) in the image here:

Question 7

What is the best interpretation of the intercept of the brainhead model?

a)The mean of headsize is 325.58 when weight of brain is zero.

b)Average brain weight is 325.58

c)The mean of brain weight is 325.58 when headsize is zero.

d)The intercept is not meaningful because head size cannot equal 0.

Question 8

What is the best interpretation of the coefficient for size_cm3 in the brainhead model?

a)A one gram increase in brain weight corresponds to a 0.26 cm^3 increase in head size..

b)Head size is not a significant predictor because the coefficient is higher than alpha = 0.05.

c)A one cm^3 increase in head size corresponds to a 0.26 gram increase in brain weight.

d)The correlation between head size and brain weight is 0.26

Question 9

What is the best interpretation of the r-squared of the brainhead model - 0.64?

a)0.64 is greater than an alpha of 0.05, therefore the model is not significant.

b)The magnitude of the effect that head size has on brain weight is 0.64 standard deviations.

c)Headsize explains 64% of the variance in brain weight.

d)Brain weight explains 64% of the variance in head size.

Question 10

What is the best interpretation of the p-value for head size in the brainhead model?

a)The p-value is less than alpha = 0.05, therefore the coefficient for head size is not significantly different from zero.

b)The p-value is less than alpha = 0.05, so head size is a statistically significant predictor of brain weight.

c)The p-value is less than alpha = 0.05, therefore headsize is not a significant predictor of brain size.

Answer 1

Question1.

a)The difference between the actual value, y, and the fitted value, y-hat

Question 2.

c)best fit line

Question3.

b)Residuals vs. Leverage

Question4

b)A violation of the assumption of constant variance

Question5

b)increase by 34%

Question6.

c)can be any units

Question7

d)The intercept is not meaningful because head size cannot equal 0

Question8

c)A one cm^3 increase in head size corresponds to a 0.26 gram increase in brain weight.

Question9

c)Headsize explains 64% of the variance in brain weight

Question10

c)The p-value is less than alpha = 0.05, therefore headsize is not a significant predictor of brain size