Alternate Hypothesis H a: The population correlation coefficient IS significantly DIFFERENT FROM zero.There IS NOT a significant linear relationship(correlation) between x and y in the population. Null Hypothesis H 0: The population correlation coefficient IS NOT significantly different from zero.If r is significant and if the scatter plot shows a linear trend, the line may NOT be appropriate or reliable for prediction OUTSIDE the domain of observed x values in the data.If r is not significant OR if the scatter plot does not show a linear trend, the line should not be used for prediction.If r is significant and the scatter plot shows a linear trend, the line can be used to predict the value of y for values of x that are within the domain of observed x values.Therefore, we CANNOT use the regression line to model a linear relationship between x and y in the population. X and y because the correlation coefficient is not significantly different from zero.” What the conclusion means: There is not a significant linear relationship between x and y. If the test concludes that the correlation coefficient is not significantly different from zero (it is close to zero), we say that correlation coefficient is “not significant.”Ĭonclusion: “There is insufficient evidence to conclude that there is a significant linear relationship between We can use the regression line to model the linear relationship between x and y in the population. What the conclusion means: There is a significant linear relationship between x and y. If the test concludes that the correlation coefficient is significantly different from zero, we say that the correlation coefficient is “significant.”Ĭonclusion: There is sufficient evidence to conclude that there is a significant linear relationship between x and y because the correlation coefficient is significantly different from zero. We decide this based on the sample correlation coefficient r and the sample size n. Ρ is “close to zero” or “significantly different from zero”. The hypothesis test lets us decide whether the value of the population correlation coefficient
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