Consider the applications for home mortgages data in the file of P12_04.xlsx. Use multiple regression to develop an equation that can be used to predict future applications for home mortgages (hint: use dummy variables for the quarters and create a time variable for the quarter numbers)

4. ?? , ? = 1, . . . , ? are i.i.d. and has p.d.f. ?(?) = { 0 ? < 0 ??−? + (1 − ?)2? −2? ? ≥ 0 , here 0 ≤ ? ≤ 1. Write down the likelihood function. (10 points) When ? = 1, write down the MLE of ?. (10 points) When ? = 1, write down the bias and variance of the MLE of ?. (10 points)

Suppose the index model for stocks 1 and 2 has the following results
??1 =2%+0.8???? +??1,??2 =?1%+1.1???? +??2,???? =20%.
The standard deviations of ??1 and ??2 are 20% and 25% respectively.

(1) Calculate the standard deviation of stock 1 and stock 2.

(2) What is the covariance between each stock and the market index.

(3) What are the covariance and correlation coefficient between these two stocks?

(4) Break down the variance of each stock into its systematic and firm-specific component.

The data below id from 128 recent sales in Mid City. For each sale, it shows the neighborhood (1, 2, or 3) of the house, # of offers made on the house, sq. footage, whether house is primarily made of brick, # of bathrooms, # of bedrooms, & selling price. Â Neghborhoods 1 & 2 are traditional, 3 is newer/more prestigious. Use regression to estimate & interpret the pricing structure of houses in Mid City.

Q4. Based on the regression of SqFt on Price, each 1 SqFt increase raises the Price by ______.

Clean Chips is a manufacturer of prototype chips based in Dublin, Ireland. Next year, in 2019, Clean Chips expects to deliver 700 prototype chips at an average price of $52,000. The plant cannot produce these prototype chips annually in the plant’s current condition. To meet future demand, Clean Chips must either modernize the plant or replace it. The old equipment is fully depreciated and can be sold for $4,450,000 if the plant is replaced. If the plant is modernized, the costs to modernize it are to be capitalized and depreciated over the useful life of the updated plant. The old equipment is retained as part of the modernize alternative. The following data on the two options are available:

Modernize Replace

Initial Investment in 2019 $ 36,800,000 $ 61,700,000

Terminal Disposal Value in 2025 $ 7,000,000 $ 17,000,000

Useful Life 7 Years 7 Years

Total annual cash variable costs per chip $ 35,500 $ 26,000

Clean Chips uses straight-line depreciation, assuming zero terminal disposal value. For simplicity, we assume no change in prices or costs in future years. The investment will be made at the beginning of 2019, and all transactions thereafter occur on the last day of the year. Clean Chips’ required rate of return is 10%. Clean Chips has a special waiver on income taxes until 2026.

Required:

1. Calculate net present value of the modernize and replace alternatives.

2. Which alternative should Clean Chips choose?

3. What factors should Clean Chips consider in choosing between the alternatives?

Show that the set ℝ2R2, equipped with operations

(?1,?1)+˜(?2,?2)=(?1+?2+1,?1+?2−1)(x1,y1)+~(x2,y2)=(x1+x2+1,y1+y2−1)

? ⋅˜ (?,?)=(??+?−1,??−?+1)

(1)defines a vector space over ℝR.

(2)Show that the vector space ?V defined in question 1 is isomorphic to ℝ2R2 equipped with its usual vector space operations. This means you need to define an invertible linear map ?:?→ℝ2T:V→R2.

1) You must implement a recursive Quicksort algorithm that will read integers from the attached MyList.txt file. Your algorithm must sort the list(integers)in ascending order.

2)You must implement a recursive Mergesort algorithm that will read integers from the attached MyList.txt file. Your algorithm must sort the list(integers)in ascending order.

My List.txt Values

7

3

4

1

4

4

9

9

4

8

4

5

3

9

2

3

7

0

6

4

4

5

0

1

9

2

1

7

4

7

8

7

8

3

6

3

5

9

7

3

7

8

8

2

5

9

1

2

7

2

0

1

7

5

4

3

0

5

9

2

0

7

8

9

8

4

8

2

9

2

2

1

1

5

7

5

7

5

8

7

3

2

7

8

0

1

5

1

7

6

9

2

9

6

3

9

2

6

0

5

8

9

7

5

3

5

4

2

4

5

7

7

6

9

7

1

9

4

2

9

1

1

6

4

6

5

7

3

5

1

6

8

5

9

3

5

The data below id from 128 recent sales in Mid City. For each sale, it shows the neighborhood (1, 2, or 3) of the house, # of offers made on the house, sq. footage, whether house is primarily made of brick, # of bathrooms, # of bedrooms, & selling price. Neghborhoods 1 & 2 are traditional, 3 is newer/more prestigious. Use regression to estimate & interpret the pricing structure of houses in Mid City.

Q1. Predict Price (dependent variable) as a function of Nbhd (independent variable). Is the relationship statistically significant i.e. can we reject the null hypothesis that the mean price is the same across all neighborhoods? YES or NO

The data below id from 128 recent sales in Mid City. For each sale, it shows the neighborhood (1, 2, or 3) of the house, # of offers made on the house, sq. footage, whether house is primarily made of brick, # of bathrooms, # of bedrooms, & selling price. Â Neghborhoods 1 & 2 are traditional, 3 is newer/more prestigious. Use regression to estimate & interpret the pricing structure of houses in Mid City.

Q2. Predict Price using SqFt as the independent variable. Is the relationship between these variables statistically significant? YES or NO