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What type of variables are typically used in linear regression? Two numerical variables
What does a scatterplot primarily help you do? Visualize relationships between variables
A correlation of +1 means: Perfect positive linear relationship
A correlation close to 0 suggests: Little to no linear relationship
Which statement is TRUE about correlation? Correlation does not necessarily imply causation
What does the slope represent in a regression equation? The average increase in y for a 1-unit increase in x
In the equation ŷ = 2112.35 + 155.47x, what does 155.47 represent? Average increase in revenue for each additional minute
In a regression equation, the intercept represents: Predicted y when x = 0
What is the formula for a residual? Actual value minus predicted value
What does R² measure? The proportion of variation explained by the model
An R² value of 0.655 means: 65.5% of variation in y is explained by x
What hypothesis is tested for slope significance? H0: β1 = 0
If the p-value for the slope is very small, we conclude: There is evidence of a linear relationship
What does it mean if a confidence interval for the slope includes 0? The relationship may not be statistically significant
Residual Standard Error (RSE) measures: Typical prediction mistake size
What is the main goal of Ordinary Least Squares (OLS)? Minimize squared residuals
Why are residuals squared in OLS? To prevent positive and negative errors from cancelling out
Which of the following is an assumption of linear regression? Residuals should randomly scatter around 0
A residual plot showing a curved pattern suggests: The relationship may not be linear
Homoscedasticity means: Residuals have constant spread around 0
Why are outliers dangerous in regression? They can strongly influence the slope and conclusions
If residuals are heavily skewed or have multiple peaks, this violates: Normality of residuals
Which situation is an example of extrapolation? Predicting far outside the observed data range
Which statement best describes the slope in regression? The average change in y for a 1-unit increase in x
Which of the following would MOST likely indicate a poor regression model? A visible pattern in residuals
What does a statistically significant slope tell us? There is evidence of a linear relationship
What does a correlation of -1 mean? Perfect negative linear relationship
What does a correlation of 0 mean? No linear relationship
What does a positive slope indicate? As x increases, y tends to increase
What does a negative slope indicate? As x increases, y tends to decrease
What does an R² value of 1 indicate? The model explains all variation in y
What does an R² value of 0 indicate? The model explains none of the variation in y
Why should extrapolation be used carefully? The relationship may not continue outside the observed range
What does a residual plot with random scatter suggest? The model assumptions may be reasonable
What is an outlier? A data point far from the overall pattern
Why does correlation not prove causation? Other variables may explain the relationship
What is the explanatory variable in regression called? The x-variable
What is the outcome variable in regression called? The y-variable
What type of relationship does correlation measure? Linear relationship
What happens if residuals show a pattern? The model may be inappropriate
Why are confidence intervals important? They show plausible values for the true coefficient
What does a narrow confidence interval indicate? More precision in the estimate
What does a wide confidence interval indicate? Less precision in the estimate
What happens if the regression assumptions are violated? The model results may be misleading
What does statistical significance tell us? The relationship is unlikely due to random chance
Does statistical significance guarantee practical importance? No
What does a scatterplot help identify besides relationships? Outliers and nonlinear patterns
What does “best fit line” mean? The line minimizing squared residuals
What is another name for the regression line? Least squares regression line