Question

Based on the below data what will be the value of multiple R?
Observations 8

ANOVA
df SS MS F
Regression 1 34 34 17
Residual 6 14 2
Total 7

Coefficients Standard Error t Stat P-value
Intercept 1 31.274666 3.984284 0.007248
Advertising (thousands of $) 47 6.19330674 1.610802 0.158349
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Answer

format: Number: Round to: 2 decimal places.

Answer 1

To calculate the value of the multiple R (the correlation coefficient), we need to utilize the F-statistic from the ANOVA table provided.

The formula to find the multiple R from the F-statistic is:

\[
R = \sqrt{\frac{F \cdot df_{Regression}}{F \cdot df_{Regression} + df_{Residual}}}
\]

From your data:
- \( F = 17 \)
- \( df_{Regression} = 1 \)
- \( df_{Residual} = 6 \)

Plugging in the values:

\[
R = \sqrt{\frac{17 \cdot 1}{17 \cdot 1 + 6}} = \sqrt{\frac{17}{17 + 6}} = \sqrt{\frac{17}{23}}
\]

Calculating it:

\[
R = \sqrt{0.7391304348} \approx 0.8607
\]

Now, rounding this value to two decimal places, we get:

**Multiple R: 0.86**