Given the Linear Correlation Coefficient $r$ And the Sample Size $n$ , Determine the Critical Values Of

question 22

Multiple Choice

Given the linear correlation coefficient $r$ and the sample size $n$ , determine the critical values of $r$ and use your finding to state whether or not the given $r$ represents a significant linear correlation. Use a significance level of $0.05$ .
$r = 0.767 , n = 25$

• A) Critical values: \(r = \pm 0.487\), significant linear correlation
• B) Critical values: \(r = \pm 0.396\), no significant linear correlation
• C) Critical values: \(r = \pm 0.396\), significant linear correlation
• D) Critical values: \(r = \pm 0.487\), no significant linear correlation

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Definitions:

Slope

Refers to the measure of the steepness, incline, or grade of a line, indicating the rate at which the dependent variable changes over the independent variable.

Residuals

Differences between observed and predicted values in a statistical model, representing unexplained variation.

Predicted Values

Estimates or forecasts of a variable or outcome based on a model or analysis of correlated variables.

Actual Y Values

The observed values of the dependent variable in a data set or experiment, compared against predicted values in regression analysis.