Strength of Evidence for a Linear Relationship
After performing inference for the slope of a regression line, rank the following four outcomes from strongest to weakest, based on the evidence they provide for a linear relationship: (a) the hypothesis test yields a p-value much less than 0.05; (b) the 95% confidence interval for the slope does not include 0; © the t-statistic is large in magnitude; and (d) the coefficient of determination () is high.
The 95% confidence interval for the slope does not include 0, The hypothesis test yielded a p-value much less than 0.05, The t statistic is large in magnitude, The coefficient of determination (R²) indicates that a substantial proportion of the variability in y is explained by x
The coefficient of determination (R²) indicates that a substantial proportion of the variability in y is explained by x, The t statistic is large in magnitude, The 95% confidence interval for the slope does not include 0, The hypothesis test yielded a p-value much less than 0.05
The t statistic is large in magnitude, The hypothesis test yielded a p-value much less than 0.05, The 95% confidence interval for the slope does not include 0, The coefficient of determination (R²) indicates that a substantial proportion of the variability in y is explained by x
The hypothesis test yielded a p-value much less than 0.05, The 95% confidence interval for the slope does not include 0, The t statistic is large in magnitude, The coefficient of determination (R²) indicates that a substantial proportion of the variability in y is explained by x
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