Question

The demand function for good X is 𝑄𝑥 𝑑 = 𝑎 − 𝑏𝑃𝑥 + 𝑐𝑀 + 𝑒 . Where 𝑃𝑥 is the price of good X and M is income . Least squares regression reveals that â = 8.27, bˆ = 2.14, cˆ = 0.36, 𝜎â = 5.32, 𝜎𝑏ˆ = 0.41, and 𝜎𝑐ˆ = 0.22. The R-squared is 0.35. a. Compute the t-statistic for each of the estimated coefficients. (4mks) b. Determine which (if any) of the estimated coefficients are statistically different from zero. (4mks) c. Explain, in plain words, what the R-square in this regression indicates. (

Answer 1

$Qxd=a-bPx+cm+e$

Fitting in the estimated coefficients

$Qxd=8.27-2.14Px+0.36M+e$

$ta=\frac{a}{da}=\frac{8.27}{5.32}=1.55$

$tb=\frac{b}{db}=\frac{2.14}{0.41}=5.22$

$tc=\frac{c}{dc}=\frac{0.36}{0.22}=1.64$

Where ta, tb and tc represents the t test values for a, b and c respectively.

- Only the estimated coefficients of b is statistically different from zero. This is because it's t-value (5.22) is greater than the table t-value= 2.776.

- The R-square 0.35 explains 35% of the total valuation of demand for good X in relation to price and income. The remaining 65% is attributed to the error term and other factors affecting demand.