lect19 - Review Fitting a Line to Data Interpreting the LS...

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Review Fitting a Line to Data Outline Review Fitting a Line to Data The Least Squares (LS) Regression Line Interpreting the LS Regression Line Properties of Residuals R-squared ( r 2 ) Conditions for Simple Regression 1 / 17 ISOM 2500 Lect 19: Linear Patterns

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Review Fitting a Line to Data What You Should Already Know Graphical Tools Histogram, boxplot, and scatterplot Mean, Variance, and Correlation Mean is the average value. Variance is the average squared deviation from the mean. Correlation measures the strength of linear association Normal Distribution 95% of the distribution lies within μ ± 2 σ . Normal quantile plot as a diagnostic Sampling Distribution Random sampling; sample-to-sample variation of a statistic; role of the central limit theorem (CLT); standard error of mean s / n Conﬁdence Interval: 95% CI is [estimate ± 2 se]. Interpretation. Hypothesis Testing t - statistic counts the number of se’s from conjectured value p - value measures “plausibility” of H 0 . For two-sided tests, reject H 0 at the 0.05 signiﬁcance level p - value<0.05 | t - statistic|>2 hypothesized value lies outside 95% CI 2 / 17 ISOM 2500 Lect 19: Linear Patterns
Review Fitting a Line to Data The Least Squares (LS) Regression Line Relationships in Bivariate Data How much should one expect to pay for a diamond ring with a 0.3 carat diamond? The ﬁle DiamondRings.JMP contains the price (in Singapore \$) and weight (in carats) of 48 diamond rings. 1 JMP summaries for these two variables are obtained as Do univariate summaries tell you about the relationship between weight and price? 1 The source of this data was a February 29, 1992 advertisement in the Straits Times, a Singapore newspaper. 3 / 17 ISOM 2500 Lect 19: Linear Patterns

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Review Fitting a Line to Data The Least Squares (LS) Regression Line A scatterplot reveals the relationship between weight and price 2 How would you describe the dependence between the weight and price of these diamonds? Direction? Strength? Linear? Recall (from Lecture 4) Response : the variable whose variation is of interest Explanatory variable or predictor : the variable that’s used to explain the variation in the response is the response in this example is the explanatory variable in this example The explanatory variable is placed on the x -axis and the response is placed on the y -axis in a scatterplot.
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lect19 - Review Fitting a Line to Data Interpreting the LS...

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