Model & Assumptions
The name for the variable we are trying to explain or predict.
What is the response variable?
The slope of the regression line represents this kind of change.
What is the expected change in the mean response for a one-unit increase in X?
This parameter is tested in H0:β1= 0.
What is the slope?
This statistic tells us the proportion of variation in Y explained by X.
What is R^2?
Create pseudocode for estimating a simple linear regression model predicting Y from X from data set called data1.
What is lm(Y, X, data = data1)?
This assumption about the errors is required for least squares estimates to be unbiased.
What is mean zero errors?
If the intercept is 50 in the regression of exam score on hours studied, interpret it in context.
What is "The predicted exam score for a student who studied 0 hours is 50"?
A 95% CI for the slope that includes 0 means this.
What is "There is not strong evidence of a linear relationship"?
If R^2=0.70, interpret in context.
What is "70% of the variation in Y is explained by X"?
This function is used to create all diagnostic plots for a simple linear regression model.
What is plot()?
Name two of the three conditions that must hold for a linear regression model to be valid.
What are linearity, independence, and constant variance?
A negative slope indicates this kind of relationship between X and Y.
What is a negative (or inverse) relationship?
The test statistic for slope is B_1 divided by this.
What is its standard error?
A regression of GPA on study hours has r=0.6. What is R^2?
What is 0.36 (36%)?
The line of code that we should use if randomizing or using a random number generator.
What is set.seed()?
Outliers with extreme X-values that strongly influence the regression line are called this.
What are influential points?
A regression of body fat percentage on BMI yields slope = 0.9. Interpret this value.
What is "For each 1-unit increase in BMI, predicted body fat percentage increases by 0.9 on average"?
In regression, a prediction interval is always (wider/narrower) than a confidence interval at the same X.
What is wider?
SSE = 150 and SST = 600. Compute R^2.
What is 0.75?
Load the MASS library and access airquality dataset.
Create a simple linear regression on ozone with Wind as the predictor.
From the coefficients table of the model's summary, what is the estimated values of ozone?
96.8729
If residuals vs. fitted values show a curve, which regression assumption is violated?
What is linearity?
A student’s residual is -12. What does this mean about their observed and predicted values?
What is "Their actual Y is 12 lower than predicted"?
What are:
t-test for slope: B_1 = 0
anova test: B_1 = 0
t-test for correlation: rho = 0
Residuals show increasing spread with fitted values. Which regression assumption is violated?
What is constant variance?
Load the MASS library and access airquality dataset.
Create a simple linear regression on ozone with Temp as the predictor.
From the coefficients table of the model's summary, what is the adjusted R-Squared of the model?
0.4832