The amounts of 6 restaurant bills (x) and the corresponding amounts of the tips

Question

The amounts of 6 restaurant bills (x) and the corresponding amounts of the tips (y) are given in the table below.

Use a 0.05 confidence level to find the following:
The correlation coefficient r =_____
The test statistic for a test of significant correlation t =______.  
Is there a significant correlation?
The regression equation is y^ = ____+____x
If the amount of the bill is $65, the best prediction for the amount of the tip is _____.

Explanation / Answer

X Values
= 395.39
Mean = 65.898
(X - Mx)2 = SSx = 2421.032

Y Values
= 51.48
Mean = 8.58
(Y - My)2 = SSy = 80.72

X and Y Combined
N = 6
(X - Mx)(Y - My) = 409.495

R Calculation
r = ((X - My)(Y - Mx)) / ((SSx)(SSy))

r = 409.495 / ((2421.032)(80.72)) = 0.9263

t = 4.917

The P-Value is 0.007947. The result is significant at p < 0.05.

-2.566+0.169x

Bill is $65

-2.56+0.169*65 = $8.42

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