Econ 3338

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(c) y=β₀+ β1x+u

β1 = Σxy/Σx2 = (-143.6)/(27.6) = -5.203

β₀ = ȳ - β1 x̄ = 77.3-(-5.203*24.2) = 203.213

y = 203.213 – 5.203 x + u

(d) [pic 1]

(e) ȳ = 77.3 x̄ = 24.2

Elasticity of demand = slope*(x/y) = (-5.203)*(24.2/77.3) = -1.629

Question 2

(a) This is a time series regression.

(b) [pic 2]

(c) The relationship between them is negative.

No, it does not make economic sense. Because from the equation, we can see when the price of coffee (X) equal to zero, the coffee consumption (Y) should be equal to 2.6911. However, in the real life, when the price of coffee (X) equal to zero, the coffee consumption (Y) supposed to larger than 2.6911, so the equation does not make sense.

(d) The slope is (-0.4795) that means X and Y have negative relationship. When X increase 1, Y is decrease 0.4795.

(e) No, it is not possible. Because is a sample regression function (SRF).

(f) No, I cannot. Because the price elasticity of demand equation = slope*(X/Y). However, there is not any data for X and Y.

Question 3

Y = 520.4 – 5.82 X

(a) when X = 22, Y = 520.4 – 5.82*22 = 392.36

(b) when X = 19, Y = 520.4 – 5.82*19 = 409.82

When X = 23, Y = 520.4 – 5.82*23 = 386.54

409.82 – 386.54 = 23.28

(c) when X = 21.4, Y = 520.4 – 5.82*21.4 = 395.852

(d) SSR = SER2 (n-2) = 11.52 * (100-2) = 12961

R2 = 1-SSR/SST 0.082 = 1-12961/SST SST = 13044.48

SST = ơ2 (n-1) 13044.48 = ơ2 (100-1) ơ2 = 131.76 ơ = 11.48

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