Slopes

Accept the null hypothesis

Reject the null hypothesis

Cannot determine the conclusion

Fail to reject the null hypothesis

Proportion of variance in Y explained by X.

Change in response variable per one unit increase in explanatory variable.

Average value of response variable Y when explanatory variable X equals zero.

Difference between actual and predicted values of Y.

Cannot determine the conclusion

Reject the null hypothesis

Fail to reject the null hypothesis

Accept the null hypothesis

Performing multiple linear regressions including other lifestyle factors such as diet and sleeping patterns

Calculating Pearson’s correlation coefficient between reported exercise frequency and stress levels from surveys

Using historical data on exercise routines and medical records documenting stress-related conditions

Conducting a randomized controlled trial measuring stress responses after controlled exercise interventions.

$H_{0} : \beta_{1} = 0$

$H_{0} : \beta_{1} > 0$

$H_{0} : \mu = \mu_{0}$ where $\mu$ is population mean score

$H_{0} : r = 0$ where $r$ is Pearson's correlation coefficient

There is sufficient evidence to reject the null hypothesis that the slope is zero.

The correlation between variables in the model is not significant.

A type II error has definitely been made in testing the hypothesis.

There is not enough evidence to reject the null hypothesis that the slope is zero.

n

n-2

n+1

n-1

Chi-square distribution

F-distribution

T-distribution

Normal distribution

The strength of the linear relationship as measured by the coefficient of determination ($R^2$).

The possibility of lurking or confounding variables influencing both coffee intake and productivity levels.

Ensuring that there are no outliers in data points representing coffee consumption and productivity.

Verifying that productivity is measured consistently across all participants in the study.

The probability of making a Type I error

The threshold for determining whether to reject the null hypothesis

The level of confidence in the alternative hypothesis

The probability of making a Type II error