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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