In baseball, is there a linear correlation between batting average and home run percentage? Let x represent the batting average of a professional baseball player, and let y represent the player's home run percentage (number of home runs per 100 times at bat). A random sample of n = 7 professional baseball players gave the following information.

(a) Make a scatter diagram of the data.

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(b) Use a calculator to verify that Σx = 1.949, Σx² = 0.549, Σy = 30.0, Σy² = 148.36 and Σxy = 8.687.

Compute r. (Round your answer to three decimal places.)


As x increases, does the value of r imply that y should tend to increase or decrease? Explain your answer.

Given our value of r, y should tend to increase as x increases.Given our value of r, we can not draw any conclusions for the behavior of y as x increases.     Given our value of r, y should tend to remain constant as x increases.Given our value of r, y should tend to decrease as x increases.

1. In Excel, create a 2x30 data table with the left column representing a population of prey and the right column representing a population of predators. Use the population model presented below.

Let the starting values of the model parameters be: r = 1.3, k = 1, s = .5, v = 1.6, and u = .7

Let the starting population of P = 1.1 and Q = .4

Difference equations: P[t + 1] = P[t](1 + r(1 – P[t]/K)) - sP[t]Q[t]

Qt + 1 = (1-u)Q[t] + vP[t]Q[t]

a. What does sP[t]Q[t] and vP[t]Q[t] represent?

b. Plot the values of P[t] and Q[t] in a graph.

c. Describe in words the changes in P[t] and Q[t] through time.

d. Build table in excel and describe in words what happens if you increase the growth rate of prey (r)? What about if we decrease the growth rate?

e. What does u represent? Why should u be less than 1? What happens if we make u = 1? Can you think of any biological systems in which u = 1 is a realistic assumption?

f. Create a second Excel worksheet representing another population model. Use the instructions from question 1, except that your model should now include a term to represent the amount of prey which cannot be eaten because they are hiding in refuges (just like in question 2) represented by the term: w. Also, for the predators, include a term f representing what happens if a constant, external food source contributes to the predator population.

Let w = 0.3 and let f = 0.25

g. Graph the new population levels.

h. Explore different values of w and f. Try setting w = 0, or f = 0 to see what effect each of these has individually. Describe your results.

The following table reports the Consumer Pirce Index for the Los Angeles area on a monthly basis from January 1998 to December 2000 (base year=1982-1984). Eliminating the data for 2000, use Excel to forecast the index for all of 2000 using a three-and -six month average. Which provides a better forecast for 2000 using the data provided?

rev: 09_12_2014_QC_53420

The following is average weekly per pound price data for apple pears in the US (from usda.gov) starting May. Your employer wants you to determine forecasted average weekly price for all the weeks starting in May.

1. For each period starting in May (through August 6), determine the forecasted values (round all responses to two decimal places) using:
   1. Naïve previous period
   2. Four-period moving average
   3. Four-period weighted moving average (w₁=0.35, w₂=0.3, w₃=0.25, w₄=0.10).
   4. Exponential smoothing with an α= .35. Make the assumption that the forecasted value of May 20 is equal to the actual value of May 20.

To receive any credit for filling out the above table, you must show your hand written work on attached pages. You should also double check your work using Excel (Excel for forecasting won’t be graded).

2. For the last four periods in the month of July (includes: July 8, July 15, July 22, and July 29),
   1. calculate MAD, MSE, and MAPE (ok to use Excel here), and fill out the following table

2. Which forecasting technique do you recommend the company uses? Justify your response.

Scenario: (Chest Pain, Shortness of Breath) Richard is a 65 year old client is admitted to your ward after an acute episode of chest pain. Current diagnosis is Acute episode of Unstable Angina. This is day two in the ward. Past Medical history reveals hypercholesterolemia x 10 years, DMT2 x 5 years, unstable angina x two years, coronary artery disease x two years and hypertension x six years. No relevant social or psychiatric history found.

Nurses call bell rings. As an EN you are answering the call bell. Client states that he is having sever chest pain. Verbalise your actions:

Assessment On asking Richard states that the chest pain is squeezing type at the centre of the chest radiating towards his jaw. Pain started as he was in the toilet trying to open his bowels. Richard states that he has not passed stools in the last two days. LOC: alert and oriented.

Vital signs: T= 36.2°C, PR=102/min RR=30/min BP=136/90 SaOz=98% on room air BGL 12.0 Pain: 9 out of 10

Relevant Investigations: Troponin 1 = 0.9 Troponin 2 = 1.5 Troponin 3 = 0.3 Urea = 4.Smmol/L Creatinine = 126 Micromol/L Na+ = 142 mmol/L K+= 3.1 mmol/L Ca2+ = 1.8 mmol/L Mg2+ = 0.5 MMOl/1. Current treatment plan: 4/24 Vital Signs BGLs QID + 0200am Daily ECGs Aperients PRN Analgesics and antiemetic's PRN TED stockings Toilet privileges if pain free Inform doctor about each episode of Chest Pain. Morphine and GTN as per protocol.

Based on the above scenario, please briefly write the progress note in a paragraph style not in seperate sentences.

Flexible Budgeting and Variance Analysis

I Love My Chocolate Company makes dark chocolate and light chocolate. Both products require cocoa and sugar. The following planning information has been made available:

I Love My Chocolate Company does not expect there to be any beginning or ending inventories of cocoa or sugar. At the end of the budget year, I Love My Chocolate Company had the following actual results:

Required:

1. Prepare the following variance analyses for both chocolates and the total, based on the actual results and production levels at the end of the budget year:

     a. Direct materials price variance, direct materials quantity variance, and total variance.

     b. Direct labor rate variance, direct labor time variance, and total variance.

Enter a favorable variance as a negative number using a minus sign and an unfavorable variance as a positive number.

India is the second most populous country in the world, with a population of over 1 billion people. Although the government has offered various incentives for population control, some argue that the birth rate, especially in rural India, is still too high to be sustainable. A demographer assumes the following probability distribution for the household size in India.

Compute the mean of the household size in India?

Professor Sanchez has been teaching Principles of Economics for over 25 years. He uses the following scale for grading.

Compute the variance of the numerical score.

You have $400,000 invested in a well-diversified portfolio. You inherit a house that is presently worth $200,000. Consider the summary measures in the following table:

The correlation coefficient between your portfolio and the house is 0.38.

What is the standard deviation of new portfolio which includes old portfolio and house?

Questions below are separate

1. If E(X) = 10 and E(Y) = 20, Var(X) = 3, Var(Y) = 5 and Cov(X, Y) = 10, then

what is the var(Z) where Z = 3X+2Y?

2. If E(X) = 10 and E(Y) = 20, Var(X) = 3, Var(Y) = 5 and Cov(X, Y) = 10, then

what is the mean of Z where Z = 3X+2Y?

Note that mean of Z = E(Z).

3. If correlation coefficient =0.3 and Var(X) =25 and Var(Y) = 16, then what is Cov(X, Y)?

The following is the recent historical sales of Sony HDTV at a local BestBuy store.

• Solution inputs are numbers only, no symbols or letters such as "$, (2.3), dollar".
• Numbers can be in the format of either 3000 or 3,000; 0.95 or .95
• Keep two decimals if not exact, do not round. For example, 3.24923... will be kept as 3.24, but the exact value of 0.625 will be kept as 0.625

1. Use the naive approach to forecast sales for June.  
2. Use a 4-month simple moving average to forecast sales for June.  
3. Using weighted moving average method, with weights of 0.5 one period ago, 0.3 two periods ago, and 0.2 three periods ago, to forecast sales for June.  
4. Assuming the forecast for April is 60. Use exponential smoothing, with a smoothing constant of 0.2, to forecast sales for June.  
5. Use simple linear regression y=a+bx, to first calculate the parameter value of b , then the parameter value of a  , and finally to forecast sales for June.  

Please evaluate Forecasting Method A, in terms of MAD and TS, based on the following forecasted sales, comparing to the realized actual sales.

• Solution inputs are number and letter only, no symbols such as "A., or (2.3)"
• Numbers can be in the format of either 3000 or 3,000; 0.95 or .95; negative number should be in the format of -0.8 instead of (0.8).
• Keep two decimals if not exact, do not round. For example, 3.24923... will be kept as 3.24, but the exact value of 0.625 will be kept as 0.625

1. The MAD value of forecasting method A is:  
2. The TS value of forecasting method A is:  
3. If another forecasting method B has the MAD = 4, and TS = 0.2, then which forecasting method (A or B) is better in terms of MAD value?   and which forecasting method (A or B) is better in terms of TS value?