1. We use the added variable technique to derive the variance ination factor (VIP). Consider a linear model of the form 91' =50+l31$1+l3213922+-"+}3p$a'p+zr, 5'3: 1:"'ana (1) where the errors are uncorrelated with mean zero and variance 02. Let X denote the n X p' predictor matrix and assume X is of full rank. We will derive the VIP for ip. The same derivation applies to any other coefcient simply by rearranging the columns of X. Let U denote the matrix containing the rst p' 1 columns of X and let z denote the the last column of X so that X = [U 2]. Then we can write the model in (1) as 50 x91 Y=[U z](,:J)+t-:=Ua+z6p+e with a: (2) x810. 1 Let 2 denote the vector of tted values from the least squares regression of z on the columns of U (Le. the regression of X.p on all the other variables), and let T : z 2 denote the residuals from that regression. Note that 'r' and 3 are not random, they are constant vectors obtained by linear transformations of z. (a) Show that the regression model in (2) can be rewritten in the form for some constant vector 6 of the same length as a. (Hint: z : i l 'r and 2? = U(UTU)_1UTz). (b) Show that UT? 2 0, a zero vector. (0) Obtain simplied expressions for the least squares estimators of 5 and 5?, showing, in particular, that 5,, : 'rTY/rT'r. (d) Based on Part (c) and the model assumptions, show that 0.2 ELK\"? _ is)? where :Eg-p is the LS tted value from regression X,D on the all the other predictor variables with an intercept. var(,p) : Other receipts for the couple were as follows: Dividends (all qualified dividends) $2.500 Interest income: Union Bank $ 220 State of Idaho-interest on tax refund 22 City of Boise school bonds 1.250 Interest from U.S. savings bonds 410 (not used for educational purposes) 2017 federal income tax refund received in 2018 2,007 2017 state income tax refund received in 2018 218 Idaho lottery winnings 1.100 Casino slot machine winnings 2,250 Gambling losses at casino 6.500 Other information that the Reyeses provided for the 2018 tax year. Mortgage interest on personal residence $11.081 Loan interest on fully equipped motor home 3.010 Doctor's fee for a face-lift for Mrs. Reyes 8.800 Dentist's fee for a new dental bridge for Mr. Reyes 3,500 Vitamins for the entire family 1 10 Real estate property taxes paid $ 5,025 DMV fees on motor home (tax portion) 1.044 DMV fees on family autos (tax portion) 436 Doctors' bills for grandmother 2,960 Nursing home for grandmother 10,200 Wheelchair for grandmother 1.030 Property taxes on boat 134 Interest on personal credit card 550 Interest on loan to buy public school district bonds 270 Cash contributions to church (all the contributions 6.100 were in cash and none more than $250 at any one time) Cash contribution to man at bottom of freeway off-ramp 25 Contribution of furniture to Goodwill-cost basis 4,000 Contribution of same furniture to listed above Goodwill-fair market value 410 Tax return preparation fee for 2017 taxes 625 Required Prepare a Form 1040 and appropriate schedules, Schedule A, and Schedule B for the comple- tion of the Reyes's tax return. They do not want to contribute to the presidential election cam- paign and do not want anyone to be a third-party designee. For any missing information, make reasonable assumptions. They had qualifying health coverage at all times during the year.R.PI, Inc. Income Statement For the Year Endal 1231/2019 Question 5 (20 marks) Sales fall credit 5740.030 Los: Cost of goods cold RPI, Inc. is a manufacturer and retailer of high-quality sports clothing and gear. The firm was Gross profits started several years ago by a group of serious outdoor enthusiasts who fell there was a need Less: Operating and intered expenses for a firm that could provide quality products at reasonable prices, The result was RPI. Inc. General and administrative Since its inception, the firm has been profitable with sales that last year totaled $700,000 and Depreciation assets in excess of 5400,000. The firm now finds its growing sales outstrip its ability to Total finance its inventory needs. The firm now estimates that it will need a line of credit of Profit before Interest and taxes (EBIT) $100,000 during the coming year. To finance this funding requirement, the management Lew: Inand plans to seek a line of credit with its bank. Profit before taxes $110,100 Lew: Taxes 27.100 The firm's most recent financial statements were provided to its bank as support for the Net income available firm's loan request. Joanne Peebie, a loan analyst traince for the Morristown Bank and Trust, to common stockholders 5:2 900 has been assigned the task of analyzing the firm's loan request. Lew: Cash dividenda RPI, Inc. Balance Sheets Change in retained earnings $51,100 for 12/31/18 and 12/31/19 JO18 2019 Cash $16.030 $17,000 Marketable securities 7.00.0 7,200 Accounts receivable 42,000 38,000 Inventory 50.000 93.000 Prepaid rent 1.20:0 L.LOO Total current assets $116.200 $156 300 Net plant and equipment 286.000 290.0.00 Total assets $402 20 0 Limbifities ood Stockholders Equity Accounts payable $48.000 $55.000 Notes payable 16.000 13,000 Accruals 6.004 5.000 Total current liabilities $70.00-0 $73.0100 Long-term debt $160.000 $1502000 Common stockholders* equity $ 172. 20.0 $221300 Total liabilities and equity 5402.200 $463m