r = ( ? XY - ?X ?Y / n ) / SQRT { [? X^2 - (?X)^2 / n] [? Y^2 - (?Y)^2 / n]}
Numerator of r = (1255) - (264)(48) / 8 = -329
Denominator of r = SQRT[9572 - (264)^2 / 8] * SQRT[436 - (48)^2 / 8]
= SQRT[860] * SQRT[148]
r = -329 / [29.32576] * [12.16553]

a) Correlation coefficient r = -0.9222
b) Correlation coefficient is negative ; there is a strong negative linear relationship between daily demand and price.

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b)
Linear Regression
Number of cases 8
? X = 144
? Y = 288
? X^2 = 2648
? XY = 5244
? X ? Y = 5244

b = ( ? XY - ?X ?Y / n ) / [? X^2 - (?X)^2 / n]
Numerator of b = (5244) - (144)(288) / 8 = 60
Denominator of b = [2648 - (144)^2 / 8] = 56
b = 60 / 56
Regression coefficient b = 1.07143
Constant = 16.71429

Equation : Y = 16.714+1.0714X

c)
Is it $400,000 or $40,000 ?
substitute x=40 into Y = 16.714+1.0714X and predict y.

e)
Number of cases 8
? X = 144
? Y = 288
? X^2 = 2648
? Y^2 = 10444
? XY = 5244
? X ? Y = 5244

r = ( ? XY - ?X ?Y / n ) / SQRT { [? X^2 - (?X)^2 / n] [? Y^2 - (?Y)^2 / n]}
Numerator of r = (5244) - (144)(288) / 8 = 60
Denominator of r = SQRT[2648 - (144)^2 / 8] * SQRT[10444 - (288)^2 / 8]
= SQRT[56] * SQRT[76]
r = 60 / [7.48331] * [8.7178]
Correlation coefficient r = 0.9197

d)
Coefficient of determination = r^2 = (0.9197)^2 = 0.8458
Approximately 85% of the variation in advertising can be explained by sales.

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