The following regression model was fitted for an individual with a constant term and three explanatory variables, including the lagged yearly consumption y_t-1 and two other variables, yearly income, x_1t, and yearly savings, x_2t, for over 20 years.

where
ŷ = yearly consumption (€000)
x₁ = yearly income (€000)
x₂ = yearly savings (€000)

a. Test at the 5% level the null hypothesis that the coefficient on x₁ against the coefficient ŷ is positive.
b. Determine a 95% confidence interval for the coefficient on x₁ for the entire population.
c. Calculate the total effect of the individual consumption over all current and future time period if the estimated coefficient on x₁ increases by €1,000. Interpret your result.

Transcribed Image Text:

ŷt = 21.0+ 1.5x1 + 0.75x2+ + 0.6yt-1 (0.534) (0.435) (0.216)