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- A scientist has measured quantities y, x1,and x,. She believes that y is related to x, and x2 through the equation y = ae+Px2 8, where & is a random error that is always positive. Find a transformation of the data that will enable her to use a linear model to estimate B, and B,.For a random variable x, a new random variable y can be created by applying a linear transformation y = a + bx, where a and b are constants. If the random variable x has mean μ, and standard deviation ox, then the mean, variance and standard deviation of y are given by the following formulas. Hy = a +bμx o²y=b²o²x oy = |blox The mean annual salary for employees at a company is $35,000. At the end of the year, each employee receives a $5000 bonus and a 4% raise (based on salary). What is the new mean annual salary (including the bonus and raise) for the employees? The new mean annual salary is $.For a random variable x, a new random variable y can be created by applying a linear transformation y = a + bx, where a and b are constants. If the random variable x has mean u, and standard deviation ox, then the mean, variance and standard deviation of y are given by the following formulas. Hy = a+ bux oy=b°o²x oy= lblox The mean annual salary for employees at a company is $36,000. At the end of the year, each employee receives a $3000 bonus and a 9% raise (based on salary). What is the new mean annual salary (including the bonus and raise) for the employees? The new mean annual salary is $
- Find the variance stabilizing transformation g(y) for a response variable y, if E(y) = µ_and_V(y) = √P.9. The correlation between X and Y is calculated and recorded as rxy (and rxy is negative). A linear transformation is performed on X. The linearly transformed variable is called W, where W; = (8)X;. The correlation between W and Y is calculated and recorded as rwy. In this example, rxy might be the same as rwy, but might not be rxy would definitely be the same as rwy rxy would definitely not be the same as rWY 10. The correlation between X and Y is calculated and recorded as rxXY (and rxy is positive). A linear transformation is performed on X. The linearly transformed variable is called W, where W; = (-6)X;. The correlation between W and Y is calculated and recorded as rwY. In this example,. rxy might be the same as rwy, but might not be rxy would definitely be the same as rwy rxy Would definitely not be the same as rwy A)+ |/ 11 For a random variable x, a new random variable y can be created by applying a linear transformation y = a + bx, where a andb are constants. If the random variable x has mean u, and standard deviation a, then the mean, variance and standard deviation of y are given by the following formulas. 11 Hy =a+b DL Kolgl = D 11 The mean annual salary for employees at a company is $36,000. At the end of the year, each employee receives a $4000 bonus and a 7% raise (based on salary). What is the new mean annual salary (including the bonus and raise) for the employees? 11 *.*** The new mean annual salary is $ 11 LL 11 OL 11 Next deu 12:04 PM S8'F Sunny ^ 立 0 合罗 F10 F11 PrtSc F12 וה 5. 9. 8. 9. H K.
- Assume that a population of patients contains 30% of individuals who suffer from a certain fatal syndrome Z, which simultaneously makes it uncomfortable for them to take a life-prolonging drug X. Let Z = 1 and Z = 0 represent, respectively, the presence and absence of the syndrome, Y = 1 and Y = 0 represent death and survival, respectively, and X = 1 and X = 0 represent taking and not taking the drug. Assume that patients not carrying the syndrome, Z = 0, die with probability 0.5 if they take the drug and with probability 0.5 if they do not. Patients carrying the syndrome, Z = 1, on the other hand, die with probability 0.7 if they do not take the drug and with probability 0.3 if they do take the drug. Further, patients having the syndrome are more likely to avoid the drug, with probabilities p(X = 1|Z=0) = 0.9 and P(X = 1|Z = 1) = 0.6 . Based on this model, compute the joint distributions and for all values of x, y, and z. Present the following joint distributions in tables. [Hint:…Let the equations of the regression lines be expressed as 8X - 2Y = 0 and 3Y – 2X = 9 Then the correlation between X and Y is,The variance of temperatures (Fahrenheit) in Las Vegas, Nev. is 327.84. What is this variance if temp is re-expressed in Celsius? [Hint: Conversion between Fahrenheit and Celsius is a linear transformation: Fahrenheit = Celsius*1.80 + 32, or Celsius = Fahrenheit*(1/1.80) - (32/1.80)]
