Consider the scatterplot of sample data for ten individuals and simple regression analysis performed in Q1. Using the correct degrees of freedom you obtained in Q2, you determine that the critical value in the F-distribution is 2.54 (to two decimal places). Given your observed F-statistic is 1.11, what can you conclude?

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BlackTom AI · Accepted Answer

To start, we restate the key setup: the critical F value is 2.54 (two decimals) and the observed F-statistic from the regression is 1.11. The core question is whether this observed statistic provides evidence that X is a significant predictor of Y.
Option under consideration: "There is not sufficient evidence that X is a significant predictor of Y." This statement aligns with the standard decision rule in F-tests for regression: if the observed F is less than the critical F, we fail to reject the null hypothesis that the slope coefficient(s) associated with X equal zero, meaning X does not provide statistically significant predictive power at the chosen alpha level.
Now, breaking down why the option is correct: since 1.11 < 2.54, the test statistic does not exceed the threshold needed for significance. This implies the p-value is greater than the significance level corresponding to the 2.54 critical value, so we cannot claim that X is a significant predictor.
As for potential misconceptions: some might think any nonzero F suggests some effect, but the F-distribution critical value encodes both sample size and model complexity; here the observed value fails to reach that threshold, so the evidence is not strong enough to claim significance.
If one were to incorrectly interpret the result as showing a strong relationship, that would be misguided because a lower F relative to the critical value indicates insufficient evidence against the null hypothesis. Conversely, claiming strong significance would require an observed F at or above 2.54, which we do not have.
In summary, given F = 1.11 and the critical value 2.54, the conclusion is that there is not sufficient evidence to declare X a significant predictor of Y, matching the option presented.

PSYC20009_2025_SM2 Quiz for Simple Linear Regression: Part 2

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