Explain the concept of standard error of the slope.
The standard error of the slope (SEb) measures the variability of sample slopes around the true population slope. A smaller SEb indicates a more precise estimate of the slope.
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Explain the concept of standard error of the slope.
The standard error of the slope (SEb) measures the variability of sample slopes around the true population slope. A smaller SEb indicates a more precise estimate of the slope.
Explain the importance of checking conditions (LINE) before performing inference for linear regression.
Checking conditions (Linearity, Independence, Normality, Equal Variance) ensures the validity of the inference procedures. If conditions are not met, the results of the t-test or t-interval may be unreliable.
Explain why a statistically significant slope does not necessarily imply causation.
Correlation does not equal causation. A significant slope indicates a linear association, but other factors (lurking variables, confounding variables) may be influencing the response variable.
Explain the meaning of R-squared (R2) in linear regression.
R2 represents the proportion of the variance in the response variable that is explained by the explanatory variable. A higher R2 indicates a better fit of the regression model.
Explain the concept of residuals in linear regression.
Residuals are the differences between the observed values and the predicted values from the regression line. They represent the error in the model's predictions.
What are the differences between a t-interval for slopes and a t-test for a slope?
T-interval: Estimates the range of plausible values for the true slope. | T-test: Tests a hypothesis about the value of the slope (typically if it is zero).
What are the differences between the null and alternative hypotheses in a t-test for a slope?
Null Hypothesis (H0): Assumes there is no linear relationship (slope = 0). | Alternative Hypothesis (Ha): Claims there is a linear relationship (slope ≠ 0, slope > 0, or slope < 0).
What are the differences between correlation (r) and the slope (b) of a regression line?
Correlation (r): Measures the strength and direction of a linear relationship, but is unitless and does not predict values. | Slope (b): Predicts the change in the response variable for a one-unit change in the explanatory variable and has units.
What are the differences between deterministic and predictive language when interpreting regression results?
Deterministic language: Implies a certain outcome (e.g., 'studying one more hour will increase the score by 5 points'). | Predictive language: Acknowledges variability and makes predictions (e.g., 'studying one more hour is predicted to increase the score by 5 points').
What are the differences between the standard deviation of the residuals (s) and the standard error of the slope (SEb)?
Standard deviation of residuals (s): Measures the typical distance of the observed values from the regression line. | Standard error of the slope (SEb): Measures the variability of the sample slopes around the true population slope.
What is the definition of explanatory variable?
The explanatory variable (independent variable) is plotted on the x-axis and explains the patterns seen in a scatterplot; consider it the 'cause'.
What is the definition of response variable?
The response variable (dependent variable) is plotted on the y-axis and responds to the explanatory variable; consider it the 'effect'.
What is the definition of inference?
Inference uses sample data to make predictions or test claims about a population parameter, moving from describing data to making informed decisions.
What is a t-interval for slopes?
A confidence interval used to estimate the true slope of the population regression line, providing a range of plausible values.
What is a t-test for a slope?
A hypothesis test used to determine if there is a significant linear relationship between two variables by testing if the slope is significantly different from zero.