Question

In: Statistics and Probability

Consider the following sample data for the relationship between advertising budget and sales for Product A:...

Consider the following sample data for the relationship between advertising budget and sales for Product A:

Observation 1 2 3 4 5 6 7 8 9 10
Advertising ($) 60,000 70,000 70,000 80,000 80,000 90,000 100,000 100,000 110,000 110,000
Sales ($) 363,000 432,000 417,000 502,000 483,000 537,000 614,000 625,000 653,000 666,000

What is the slope of the "least-squares" best-fit regression line?

Solutions

Expert Solution

X Y XY
60000 363000 21780000000 3600000000 1.31769E+11
70000 432000 30240000000 4900000000 1.86624E+11
70000 417000 29190000000 4900000000 1.73889E+11
80000 502000 40160000000 6400000000 2.52004E+11
80000 483000 38640000000 6400000000 2.33289E+11
90000 537000 48330000000 8100000000 2.88369E+11
100000 614000 61400000000 10000000000 3.76996E+11
100000 625000 62500000000 10000000000 3.90625E+11
110000 653000 71830000000 12100000000 4.26409E+11
110000 666000 73260000000 12100000000 4.43556E+11
Ʃx = Ʃy = Ʃxy = Ʃx² = Ʃy² =
870000 5292000 4.7733E+11 78500000000 2.90353E+12
Sample size, n = 10
x̅ = Ʃx/n = 87000
y̅ = Ʃy/n = 529200
SSxx = Ʃx² - (Ʃx)²/n = 2810000000
SSyy = Ʃy² - (Ʃy)²/n = 1.03004E+11
SSxy = Ʃxy - (Ʃx)(Ʃy)/n = 16926000000

Slope, b = SSxy/SSxx = 6.0234875

y-intercept, a = y̅ -b* x̅ = 5156.58363

Regression equation :

ŷ = 5156.5836 + (6.0235) x


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