A different analyst believes that the demand for a Starbucks cold brew COB depends on temperature in Celsius I’ and the price of Starbucks cold brew…

i. Suppose that Starbucks tends to have a sale on cold brew when the temperature is lower. Does this suggest Cov(T,P1) is positive, negative, or 0?i. Suppose that Starbucks tends to have a sale on cold brew when the temperature is lower. Does this suggest Cov(T,P1) is positive, negative, or 0?
ii. Do you think an increase in P1 would increase or decrease QCB, holding all other factors fixed?iii. Do you think ˆ β1 is a consistent estimator of ˜ β1? If not, using your previous answers, do you think it is systematically above or below ˜ β1 in a large sample? (Please pick above or below.)
iii. Do you think ˆ β1 is a consistent estimator of ˜ β1? If not, using your previous answers, do you think it is systematically above or below ˜ β1 in a large sample? (Please pick above or below.)
iv. Suppose the analyst has a richer dataset, now with prices. Specifically, the analyst has a large sample of independent and identically distributed observations of QCB,T, and P1 for each day. Can the analyst use data on prices to construct a better estimator of ˜ β1 than the previous estimator, ˆ β1? If so, describe such an estimator. (You would regress what on what?) (You may assume there are no other factors that systematically vary with T and P1. More formally, you may assume MLR.4 holds.)
A different analyst believes that the demand for a Starbucks cold brew COBdepends on temperature in Celsius I’ and the price of Starbucks cold brew PI .as well as other factors .The analyst is just interested in the extent to which an increase in temper-ature by 10C" affects the demand for a Starbucks cold brew , holding all otherfactors fixed . Let_ By denote the percentage increase in C CB for an increasein I’ by IC, holding all else fixed .The analyst has a large sample of independent and identically distributedobservations of Dog and I’ for each day . Motivated by the analyst’s question ,the analyst regresses log ( QOB ) on I , obtaining*By = 2/1 = 1 ( 108 ( Q CB,; ) – 108 ( Q CB )) ( I{ _ I)Li= 1 ( 1: – I ) 2)