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

Question

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
Submit
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