Please assist with graphs and explanation attached.

2. Copy and paste the following data into Excel:

P Q

$210.00 5415

$205.80 5553

$203.70 5783

$195.30 5958

$184.80 6115

$182.70 6266

$170.10 6581

$165.90 6856

a. Run OLS to determine the demand function as P = f(Q); how much confidence do you have in this estimated equation? Use algebra to invert the demand function to Q = f(P).

b. Using calculus to determine dQ/dP, construct a column which calculates the point-price elasticity for each (P,Q) combination.

c. What is the point price elasticity of demand when P=$210.00? What is the point price elasticity of demand when P=$173.25?

d. To maximize total revenue, what would you recommend if the company was currently charging P=$203.70? If it was charging P=$173.25?

e. Use your first demand function to determine an equation for TR and MR as a function of Q, and graph of P and MR on the vertical and Q on the horizontal axis.

f. What is the total-revenue maximizing price and quantity, and how much revenue is earned there? (Round your price to the nearest cent, your quantity to the nearest whole unit, and your TR to the nearest dollar.) Compare that to the TR when P = $210.00 and P = $173.25.

3. Let's practice time-series forecasting of new home sales. Click here (https://www.census.gov/construction/nrs/historical_data/index.html) to see the newest data in the first table: Houses Sold (Excel file is sold_cust.xls). Look at the monthly data on the "Reg Sold" tab. If you have trouble with the link, I have recreated the data in moodle in the Excel file "A3Q3 Census Housing Data."

Only keep the dates beginning in January 2006, so delete the earlier observations, and use the data through May 2021. Keep only the US data, both the seasonally unadjusted monthly (column B) and the seasonally adjusted annual (column G). Make a new column of seasonally adjusted monthly by dividing the annual data by 12. Make a column called "t" where t will go from 1 (Jan. 2006) to 185 (May 2021); make a t2 column too (since, if you look at the data, you can see sales are U-shaped; hence the quadratic). Also make a column "D" that is a dummy variable equal to one during the spring and summer months of March through August.

Determine the correlation between the unadjusted and the adjusted monthly data (=CORREL(unadjust., adjust.) in Excel), and produce scatterplots (with straight lines) of both. Do you think making a seasonal adjustment will be useful, given what you observe at this point?

Run four regressions:

1) seasonally unadjusted monthly as the dependent, and t and t2 as the independents,

2) seasonally unadjusted monthly as the dependent, and t, t2, and D as the independents,

3) seasonally adjusted monthly as the dependent, and t and t2 as the independents, and

4) seasonally adjusted monthly as the dependent, and t, t2, and D as the independents. Discuss your findings, and determine which of the four models is the best for forecasting new home sales. When interpreting your p-values, remember that, say, 1.0E-08 is 1.0 * 10^-8, which is 0.00000001. State the equation that would be used to forecast sales.

4. Your company, which specializes in bovine costumery (BullFeathers), has the following demand function:Q = a + bP + cM + dR

where Q is the quantity demanded of BullFeathers' most popular bird costume for cows, P is the price of that product, M is consumer income, and R is the price of a related product.The regression results are:

Adjusted R Square 0.8105

Independent Variables Coefficients Standard Error t Stat P-value

Intercept 9823.57 90.93 108.03 137E-42

P -4.859 2.096 -2.319 0.027

M 0.006 0.002 3.844 0.001

R 5.21 1.167 4.463 0.000

a. Discuss whether you think these regression results will generate good sales estimates for BullFeathers.

Now assume that the income is $55,613, the price of the related good is $237, and BullFeathers chooses to set the price of its product at $252.

b. What is the estimated number of units sold given the data above? (round to nearest unit; no decimals)

c. What are the values for the own-price, income, and cross-price elasticities?

d. If P increases by 5%, what would happen (in percentage terms) to quantity demanded?

e. If M increases by 3%, what would happen (in percentage terms) to quantity demanded?

f. If R decreases by 4%, what would happen (in percentage terms) to quantity demanded?