SAT College

11.6 A mathematics placement test is given to all entering freshmen at a small college. A
student who receives a grade below 35 is denied admission to the regular mathematics
course and placed in a remedial class. The placement test scores and the final grades for
20 students who took the regular course were recorded as follows:
Placement Test : 50 35 35 40 55 65 35 60 90 35 90 80 60 60 60 40 55 50 65 50
Course Grade : 53 41 61 56 68 36 11 70 79 59 54 91 48 71 71 47 53 68 57 79
(a) Plot a scatter diagram.
(b) Find the equation of the regression line to predict course grades from placement test scores.
(c) Graph the line on the scatter diagram.
(d) If 60 is the minimum passing grade, below which placement test score should students in the future be denied admission to this course?

Answers

Answer 1

Answer:

To solve this problem, we can use linear regression to find the equation of the regression line that predicts course grades from placement test scores. Let's go through the steps:

(a) Plotting the scatter diagram:

Placement Test (x-axis): 50 35 35 40 55 65 35 60 90 35 90 80 60 60 60 40 55 50 65 50

Course Grade (y-axis): 53 41 61 56 68 36 11 70 79 59 54 91 48 71 71 47 53 68 57 79

We can plot these points on a graph to visualize the data.

(b) Finding the equation of the regression line:

We can use the least squares method to find the equation of the regression line.

Step 1: Calculate the means of the placement test scores (x) and course grades (y):

mean_x = (50 + 35 + 35 + 40 + 55 + 65 + 35 + 60 + 90 + 35 + 90 + 80 + 60 + 60 + 60 + 40 + 55 + 50 + 65 + 50) / 20 = 55

mean_y = (53 + 41 + 61 + 56 + 68 + 36 + 11 + 70 + 79 + 59 + 54 + 91 + 48 + 71 + 71 + 47 + 53 + 68 + 57 + 79) / 20 = 57.9

Step 2: Calculate the deviations from the means for each data point:

(x - mean_x) and (y - mean_y)

-5 -20 -20 -15 0 10 -20 5 35 -20 35 25 5 5 5 -15 0 -5 10 -5

-4 -17 3 -1 10 -21 -46 12 21 1 -3 33 -9 13 13 -10 -4 10 -0 21

Step 3: Calculate the product of the deviations:

(x - mean_x) * (y - mean_y)

20 340 -60 15 0 -210 920 60 735 -20 -105 825 -45 65 65 150 0 -50 0 105

Step 4: Calculate the squared deviations of x:

(x - mean_x)^2

25 400 400 225 0 100 400 25 1225 400 1225 625 25 25 25 225 0 25 100 25

Step 5: Calculate the equation of the regression line:

The slope (b) of the regression line is given by:

b = Σ((x - mean_x) * (y - mean_y)) / Σ((x - mean_x)^2)

b = (20 + 340 - 60 + 15 + 0 - 210 + 920 + 60 + 735 - 20 - 105 + 825 - 45 + 65 + 65 + 150 + 0 - 50 + 0 + 105) / (25 + 400 + 400 + 225 + 0 + 100 + 400 + 25 + 1225 + 400 + 1225 + 625 + 25 + 25 + 25 + 225 + 0 + 25 + 100 + 25)

b = 4115 / 10275 ≈ 0.400

The y-intercept (a) of the regression line can be calculated as:

a = mean_y - b * mean_x

a = 57.9 - 0.400 * 55 ≈ 37.9

Therefore, the equation of the regression line is:

Course Grade = 0.400 * Placement Test + 37.9

(c) Graphing the line on the scatter diagram:

We can plot the regression line on the scatter diagram from part (a) to visualize the relationship between the placement test scores and course grades.

(d) Finding the placement test score for the minimum passing grade:

If 60 is the minimum passing grade, we need to find the corresponding placement test score using the equation of the regression line:

60 = 0.400 * Placement Test + 37.9

Subtracting 37.9 from both sides:

22.1 = 0.400 * Placement Test

Dividing both sides by 0.400:

Placement Test = 22.1 / 0.400 ≈ 55.25

Therefore, students in the future should be denied admission to this course if their placement test score is below approximately 55.25.

Related Questions

Other Questions
Which answer is correctThe ITCZ is the convergence of: A. Polar Easterlies B. Westerlies C. Tropical Easterlies D. Tropical Westerlies Reset Selection Assess the strategy of integration vs outsourcing for Pepsi in securing raw material for its chip plants in China. a line passes through the point (-3, -5) and has the slope of 4. write and equation in slope-intercept form for this line. On January 2, 2021, Salamone Furniture purchased display shelving for $9,000 cash, expecting the shelving to remain in service for five years. Salamone depreciated the shelving on a double-declining-balance basis, with $1,800 estimated residual value. On August 31, 2022, the company sold the shelving for $2,200 cash. Read the requirement. Start by recording depreciation expense on the shelving for 2022.Required:Record both the depreciation expense on the shelving for 2022 and its sale in August. Your team is composed of the Owner of a motor-racing circuit called the Bugatti Circuit in Le Mans in France, the Director, the Finance Director and the Marketing Director.Roland Gumpert wishes to rent your racing circuit for one day to showcase his new creation, 2021 Roland Gumpert Nathalie. You, The Bugatti Circuit, have been approached by the car manufacturer and have discussed with them on the phone and by emails over the last few months. The person you spoke with was not clear enough in explaining their project, and you hope that this meeting will clarify their needs. They are traveling to France to negotiate with you in few weeks. Your usual daily rate is 100,000 EUR for the exclusivity. They have mentioned that they would like the exclusive use on October 9, next year, which is not a good date for you as Porsche has already rented the racing circuit for 4 days. Your aim is to try to convince them to instead accept a date in September. Also, the rule is to rent the racing circuit for a minimum of three days. However, the car manufacturers mentioned a limited budget and you will have to decide if you may grant an exception. Fields Enterprises has 70,000 ordinary shares outstanding. It declares a 1.5 per share cash dividend on November 1 to shareholders of record on December 1. The dividend is paid on December 31. 1. What are the accounts that will be used on the declaration date? 2. What are the accounts that will be used on the record date? 3. What are the accounts that will be used on the payment date? 4. Prepare the entries on the appropriate dates to record the declaration and payment of the cash dividend. Suppose Y is the annual income, X is the number of years of education, and D is a dummy variable equaling 1 when a person is male. In a linear regression of Y on X and D, we estimate a coefficient of 3 for X and -4 for D. Then:a. The effect of being female is to lower income by 4.b. The effect of being male is to raise income by 4, holding education constant.c. The effect of being female is to raise income by 4, holding education constant.d. The effect of being female is to raise income by 4. After visiting several automobile dealerships, Richard selects the used car he wants. He likes its $15,300 price, but financing through the dealer is no bargain. He has $3,000 cash for a down payment, so he needs an $12,300 loan. In shopping at several banks for an installment loan, he learns that interest on most automobile loans is quoted at add-on rates. That is, during the life of the loan, interest is paid on the full amount borrowed even though a portion of the principal has been paid back. Richard borrows $12,300 for a period of four years at an add-on interest rate of 10 percent. a. What is the total interest on Richard's loan? Note: Do not round intermediate calculations. Round your answer to the nearest whole number. b. What is the total cost of the car? Note: Do not round intermediate calculations. Round your answer to the nearest whole number. c. What is the monthly poyment? Note: Do not round intermediate calculations. Round your answer to the nearest whole number. d. What is the annual percentage rate (APR)? Note: Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Consider the following. +1 f(x) = {x+ if x = -1 if x = -1 x-1 y 74 2 X -2 -1 2 Use the graph to find the limit below (if it exists). (If an answer does not exist, enter DNE.) lim, f(x) which partition management utility can be used to define and change various different guid example of a real-world problem you solved that required analysis.example of a real-world problem you solved that required decision making.example of a real-world problem you solved that required problem solving. Which of the following is a way that goals can be more effective?a) leaving golas in a more genatalized formb) only setting long term goalsc) examining goals closely to ensure that they have necessary componentsd) limiting goals to only one area of your life Consider the following oligopolistic market. In the first stage. Firm 1 chooses quantity 41. Firms 2 and 3 observe Firm 1's choice, and then proceed to simultaneously choose q2 and q3, respectively. Market demand is given by p(q) = 100 - Q and Q = 91 +92 +93. Firm 1's costs are c(91) = 691. firm 2's costs are c2(22) = 1q2 and firm 3's costs are c3(93) = 193. Starting from the end of the game, you can express Firm 2's best response function in terms of q and q3, and you can similarly express Firm 3's best response function in terms of q1 and 22. Using these answer the following questions. a) If Firm 1 chooses q = 3, what quantity will Firm 2 choose? b) If Firm 1 chooses q1 = 100, what quantity will Firm 2 choose? c) In the subgame perfect Nash equilibrium of this game, firm 1 produces what quantity? d) In the subgame perfect Nash equilibrium of this game firm 2 and firm 3 each produce what quantity? A Nacho Cheese company is considering hiring new VP of Marketing away from their main competitor. In the past, the company has had difficulty having the executives they've hired stick around longer than a year or two, and the performance of these recruits has only been moderately successful for the firm. As a result, the VP of HR wants to create a better contract that will help ensure this new hire seeks to maximize shareholder wealth rather than treating the company expense account like an ATM.Please name and describe three such provisions in the contract that would help meet that goal AND explain how they help to meet those goals.*Responses can be no less than 350 words. all of the following are true regarding bank statements except True or False/Explain: The Production Possibilities Frontier (PPF) Model and the Consumer Budget Constraint (CBC) Model explain the choices of firms and households. How do you record a sales tax payment in QuickBooks Online?Taxes > Sales Tax > Prepare return > View report > Enter payment amount, date and bank account > Record payment+ New > File Sales Tax > Enter payment amount, date and bank account > Record paymentTaxes > Sales Tax > View return > Record payment > Enter payment amount, date and bank account > Record payment+ New > File Sales Tax > Select state > Enter adjustment > Enter date and bank account > Record paymentTaxes > Sales Tax > View return > Select link for state website > Enter adjustments if needed > Enter payment date > Record payment Do this in two ways: (a) directly from the definition of the observability matrix, and (b) by duality, using Proposition 4.3. Proposition 5.2 Let A and T be nxn and C be pxn. If (C, A) is observable and T is nonsingular, then (T-AT, CT) is observable. That is, observability is invariant under linear coordinate transformations. Proof. The proof is left to Exercise 5.1. During 2020, Apple Corporation had the following share transactions:- Acquired 2,450 ordinary shares to be held as treasury shares for 110,250- Acquired additional 950 ordinary shares at 42.50 per share to be held as treasury shares- Sold 2,590 treasury shares at 40 per shareBy how much would total accumulated profits change because of the above transactions? Encode the answer as a negative if it's a decrease. A firm has the following capital structure. The corporate tax rate is 21%. Determine the after-tax weighted average cost of capital for the firm.Type Amount Return WeightMortgages (debt) 25,000,000 0.05 0.053Bonds 200,000,000 0.08 0.213Common Stock 175,000,000 0.1 0.372Preferred Stock 50,000,000 0.08 0.106Retained Earnings 120,000,000 0.12 0.255Group of answer choices1. 7.59%2. 9.19%3. 9.61%4. 5.17%Please show workings. thank you