Consider the scatterplot of sample data for ten individuals and simple regression analysis performed in Q1.

The R2 value is for your sample is 0.122, and the observed F-statistic is 1.11.

To determine whether R2 is statistically significant, you decide to compare your observed F-statistic to the critical value in the F-distribution. To find this critical value, you need to first calculate the appropriate degrees of freedom. The formulas are:

df1 = k

df2 = n - k - 1

(where k = number of independent variables, and n = sample size)

What are the degrees of freedom for this sample?

Question

Consider the scatterplot of sample data for ten individuals and simple regression analysis performed in Q1.

The R2 value is for your sample is 0.122, and the observed F-statistic is 1.11.

To determine whether R2 is statistically significant, you decide to compare your observed F-statistic to the critical value in the F-distribution. To find this critical value, you need to first calculate the appropriate degrees of freedom. The formulas are:

df1 = k

df2 = n - k - 1

(where k = number of independent variables, and n = sample size)

What are the degrees of freedom for this sample?

BlackTom AI · Accepted Answer

The problem describes a simple regression with ten observations (n = 10) and a single independent variable (k = 1). To determine the F-test degrees of freedom, we use df1 = k and df2 = n - k - 1.

First, identify df1: since there is one predictor in a simple regression, df1 = k = 1.

Next, compute df2: df2 = n - k - 1 = 10 - 1 - 1 = 8.

So the degrees of freedom are df1 = 1 and df2 = 8. This matches the general interpretation that df1 corresponds to the number of predictors, and df2 corresponds to the residual degrees of freedom after accounting for the predictors and the intercept in the model.

PSYC20009_2025_SM2 Quiz for Simple Linear Regression: Part 2

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