Kilimani Company Limited owns and sells houses around Nyashishi area in Mwanza. Assume further that the city council has built a new garbage collection area in Nyashishi. The following equation relates housing prices (price) to distance from the recently built garbage collection point (dist). \[ \log (\text { price })=9.40+0.312 \log \text { (dist) } \] \[ n=135, R^{2}=0.162 \] a) Interpret the coefficient on \( \log ( \) dist). Is the sign of this estimate what you expect it to be? ( 7.5 marks) b) What other factors about a house affect its price? ( 7.5 marks) c) How much variation in the dependent variable price is explained by the independent variable distance? (Hint: utilize the \( R \)-squared.) ( 7.5 marks)

Below is a detailed explanation of each part. ────────────────────────────── a) Interpreting the Coefficient on log(dist) The regression equation is given as:   log(price) = 9.40 + 0.312 log(dist) Here, the coefficient on log(dist) is 0.312. Because both the dependent and independent variables are in logarithms, this coefficient tells us the elasticity of house prices with respect to distance from the garbage collection area. In other words, a 1% increase in distance from the garbage collection point is associated with an average increase in house price of about 0.312%. Is the sign as expected? Yes. Since the garbage collection area is likely seen as a nuisance, houses closer to it might be less desirable (and hence less expensive). The positive coefficient indicates that as the distance increases (i.e., the house is farther away from the garbage collection point), the house price tends to be higher, which is what we would anticipate. ────────────────────────────── b) Other Factors that Might Affect House Prices House prices are influenced by a variety of factors other than just the distance from undesirable amenities. Some of these factors include: • Size or Square Footage – Larger houses or lots generally command higher prices. • Number of Bedrooms and Bathrooms – More rooms typically increase the value. • Age and Condition – Newer or well-maintained houses tend to be priced higher. • Location – Proximity to good schools, shopping centers, transportation, parks, and other neighborhood amenities. • Neighborhood Quality – Includes factors like safety, public services, and overall desirability. • Architectural Style and Interior Quality – Unique designs or high-quality finishes may increase prices. • Market Conditions – Broader economic factors and supply and demand in the housing market. • Environmental Factors – Aside from the garbage collection point, factors such as noise, pollution, and scenic quality can also play a role. ────────────────────────────── c) Variation in Price Explained by Distance The R² value provided is 0.162. In the context of a regression, R² measures the proportion of the variation in the dependent variable that is explained by the independent variable(s) in the model. Since R² = 0.162, this means that approximately 16.2% of the variation in log(price) is explained by log(dist). In other words, when we use the distance from the garbage collection area to predict the house price, we are accounting for 16.2% of the variability in house prices. The remaining 83.8% of the variation is explained by other factors not included in this simple regression model. ────────────────────────────── Summary Answer a) The coefficient of 0.312 means that a 1% increase in the distance from the garbage collection point is associated with a 0.312% increase in the price of a house. This positive sign is as expected since being further away from a potentially undesirable garbage collection area should make a house more attractive and hence more expensive. b) Other factors affecting house prices could include the size of the house, number of rooms, age, condition, location (access to amenities, schools, and employment centers), architectural style, neighborhood characteristics, market conditions, and environmental quality, among others. c) With an R² of 0.162, about 16.2% of the variation in the (log of) house prices is explained by the (log of) distance from the garbage collection area.