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).
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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.
What is the general form of the least-squares regression line equation?
y^=a+bx, where y^ is the predicted value, a is the y-intercept, and b is the slope.
How do you calculate the correlation coefficient (r) from R-squared?
r=±R2. The sign of r matches the sign of the slope.
What is the formula for the test statistic (t) in a t-test for the slope?
t=SEbb−0, where b is the sample slope and SEb is the standard error of the slope.
What is the formula for the confidence interval for the slope (b)?
b±t[objectObject], where b is the sample slope, t^ is the critical t-value, and SEb is the standard error of the slope.
How to calculate degrees of freedom (df) for t-tests and t-intervals for slopes?