STAT-S 300 Lecture Notes - Lecture 29: Standard Deviation, Test Statistic, Normal Distribution
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Population regression line- also called true regression line; for population data: uses all observations in population to calculate o. Sample regression line- also called estimated regression line; for sample data; used to estimate or test claim about true line: uses data from an srs or experiment o. Or: predicts response variable from explanatory variable. Conditions for regression inference: linear- actual relationship between and is linear. For any fixed value of , mean response , falls on true regression line. Check scatterplot (linear) or residual plot (random scatter: independent- individual observations are independent. If experiment, note how data were produced: normal- for any fixed value of , response variable varies according to normal distribution. Check histogram of residuals (bell curve) or normal probability plot of residuals (linear: equal variance- standard deviation of (called ) is same for all x-values. Check scatter plot of residuals (even distribution: random- data produced from well-designed random sample or experiment.
