Like the ratio estimator, a regression estimator can also be used to improve the precision of the estimate. Ratio estimation works well if data are well fit by a straight line through the origin (Lohr). However, this may not always be the case. Data may appear to have a linear fit that may not pass through the origin. In this case, y=B0+B1x would provide a better fit. Given a sample size n, the regression coefficient and intercept can be estimated as B^1=iS(xix)2iS(xix)(yiy)andB^0=yB^1xY can be estimated when X is known using the regression line such that y^=B^0+B^1X. Prove the following: a. E(y^Y)=Cov(B^1,x) b. MSE(y^)(1f)nSy2(1R2), where R=(N1)SxSyi=1N(xiX)(yiY).

1. Martinez Hardware Store Inc. completed the following merchandising transactions in the month
of May 2022. At the beginning of May, Martinez's ledger showed Cash of $8,400 and Common
Shares of $8,400. May 1 Purchased merchandise on account from Hilton Wholesale Supply for
$8,400, terms 2/10,n/30. 2 Sold merchandise on account for $4,500, terms n/30. The cost of the
merchandise sold was $3,600. 5 Received credit from Hilton Wholesale Supply for merchandise
returned $260. 9 Received collections in full from customers billed on May 2. 10 Paid Hilton
Wholesale Supply in full, less discount. 11 Purchased supplies for cash $900. 12 Purchased
merchandise for cash $2,700. 15 Received $300 refund for return of poor-quality merchandise
from supplier on cash purchase. 17 Purchased merchandise from Northern Distributors for
$2,500, terms 2/10,n/30. 19 Paid freight on May 17 purchase $300. 24 Sold merchandise for cash
$5,300. The cost of the merchandise sold was $4,200. 25 Purchased merchandise from Toolware
Inc. for $800, terms 3/10,n/30. 27 Paid Northern Distributors in full, less discount. 29 Made
refunds to cash customers for returned merchandise $120. The returned merchandise was
returned to inventory and had cost $92 31 Sold merchandise on account for $1,200, terms n/30.
The cost of the merchandise sold was $900. Martinez Hardware uses a perpetual inventory
system and expects a return rate of 3% on all sales.
Record the above transactions. (Credit account titles are automatically indented when the amount
is entered. Do not indent manually. If no entry is required, select "No Entry" for the account
titles and enter 0 for the amounts. Round answers to the nearest whole dollar, e.g. 5,775. List all
debit entries before credit entries.)