Question

4) The correlation coefficient r is a sample statistic. What does it tell us about the value of the population correlation coefficient ρ (Greek letter rho)? You do not know how to build the formal structure of hypothesis tests of ρ yet. However, there is a quick way to determine if the sample evidence based on ρ is strong enough to conclude that there is some population correlation between the variables. In other words, we can use the value of r to determine if ρ ≠ 0. We do this by comparing the value |r| to an entry in the correlation table. The value of α in the table gives us the probability of concluding that ρ ≠ 0 when, in fact, ρ = 0 and there is no population correlation. We have two choices for α: α = 0.05 or α = 0.01. 10-table-06.gif

(a) Look at the data below regarding the variables x = age of a Shetland pony and y = weight of that pony. Is the value of |r| large enough to conclude that weight and age of Shetland ponies are correlated? Use α = 0.05. (Use 3 decimal places.) x 3 6 12 20 21 y 60 95 140 170 174 r= critical r=

(b) Look at the data below regarding the variables x = lowest barometric pressure as a cyclone approaches and y = maximum wind speed of the cyclone. Is the value of |r| large enough to conclude that lowest barometric pressure and wind speed of a cyclone are correlated? Use α = 0.01. (Use 3 decimal places.) x 1004 975 992 935 980 938 y 40 100 65 145 66 148 r= critical r=

5) Previously, you studied linear combinations of independent random variables. What happens if the variables are not independent? A lot of mathematics can be used to prove the following: Let x and ybe random variables with means μx and μy, variances σ2x and σ2y, and population correlation coefficient ρ(the Greek letter rho). Let a and b be any constants and let w = ax + by for the following formula. μw = aμx + bμy σ2w = a2σ2x + b2σ2y + 2abσxσyρ In this formula, r is the population correlation coefficient, theoretically computed using the population of all (x, y) data pairs. The expression σxσyρ is called the covariance of x and y. If x and y are independent, then ρ = 0 and the formula for σ2w reduces to the appropriate formula for independent variables. In most real-world applications the population parameters are not known, so we use sample estimates with the understanding that our conclusions are also estimates. Do you have to be rich to invest in bonds and real estate? No, mutual fund shares are available to you even if you aren't rich. Let x represent annual percentage return (after expenses) on the Vanguard Total Bond Index Fund, and let y represent annual percentage return on the Fidelity Real Estate Investment Fund. Over a long period of time, we have the following population estimates. μx ≈ 7.35, σx ≈ 6.58, μy ≈ 13.17, σy ≈ 18.59, ρ ≈ 0.421

(b) Suppose you decide to put 65% of your investment in bonds and 35% in real estate. This means you will use a weighted average w = 0.65x + 0.35y. Estimate your expected percentage return μw and risk σw. μw = σw = (c) Repeat part (b) if w = 0.35x + 0.65y. μw = σw =

6) In the least-squares line ŷ = 5 + 7x, what is the marginal change in ŷ for each unit change in x?

7) The following Minitab display gives information regarding the relationship between the body weight of a child (in kilograms) and the metabolic rate of the child (in 100 kcal/ 24 hr). Predictor Coef SE Coef T P Constant 0.8543 0.4148 2.06 0.84 Weight 0.41969 0.02978 13.52 0.000 S = 0.517508 R-Sq = 95.2%

(a) Write out the least-squares equation. y hat = + x

(b) For each 1 kilogram increase in weight, how much does the metabolic rate of a child increase? (Use 5 decimal places.)

(c) What is the value of the correlation coefficient r? (Use 3 decimal places.)

Answer #1

(6) Ans: 7

(7)

The correlation coefficient r is a sample statistic.
What does it tell us about the value of the population correlation
coefficient ρ (Greek letter rho)? You do not know how to
build the formal structure of hypothesis tests of ρ yet.
However, there is a quick way to determine if the sample evidence
based on ρ is strong enough to conclude that there is some
population correlation between the variables. In other words, we
can use the value of r...

The correlation coefficient r is a sample statistic.
What does it tell us about the value of the population correlation
coefficient ρ (Greek letter rho)? You do not know how to
build the formal structure of hypothesis tests of ρ yet.
However, there is a quick way to determine if the sample evidence
based on ρ is strong enough to conclude that there is some
population correlation between the variables. In other words, we
can use the value of r...

Previously, you studied linear combinations of independent
random variables. What happens if the variables are not
independent? A lot of mathematics can be used to prove the
following: Let x and y be random variables with means μx and μy,
variances σ2x and σ2y, and population correlation coefficient ρ
(the Greek letter rho). Let a and b be any constants and let w = ax
+ by for the following formula.
μw = aμx + bμy
σ2w = a2σ2x +...

Examine the computation formula for r, the sample
correlation coefficient.
(a) In the formula for r, if we exchange the symbols
x and y, do we get a different result or do we
get the same (equivalent) result? Explain your answer.
The result is different because the formula is dependent on the
symbols.The result is the same because the formula is dependent on
the symbols. The result is the same
because the formula is not dependent on the symbols.The result is...

Examine the computation formula for r, the sample
correlation coefficient.
(a) In the formula for r, if we exchange the symbols
x and y, do we get a different result or do we
get the same (equivalent) result? Explain your answer.
The result is the same because the formula is not dependent on
the symbols.The result is different because the formula is
dependent on the symbols. The result is
different because the formula is not dependent on the symbols.The
result is...

Examine the computation formula for r, the sample
correlation coefficient.
(a) In the formula for r, if we exchange the symbols
x and y, do we get a different result or do we
get the same (equivalent) result? Explain your answer.
The result is the same because the formula is not dependent on
the symbols.The result is different because the formula is
dependent on the symbols. The result is
different because the formula is not dependent on the symbols.The
result is...

Examine the computation formula for r, the sample
correlation coefficient.
(a) In the formula for r, if we exchange the symbols
x and y, do we get a different result or do we
get the same (equivalent) result? Explain your answer.
The result is the same because the formula is dependent on the
symbols.The result is different because the formula is not
dependent on the symbols. The result is
different because the formula is dependent on the symbols.The
result is the...

Examine the computation formula for r, the sample
correlation coefficient.
1. In the formula for r, if we exchange the symbols
x and y, do we get a different result or do we
get the same (equivalent) result? Explain your answer.
(A) The result is the same because the formula is not dependent
on the symbols.
(B) The result is different because the formula is not dependent
on the symbols.
(C) The result is different because the formula is dependent...

Examine the computation formula for r, the sample correlation
coefficient. (a) In the formula for r, if we exchange the symbols x
and y, do we get a different result or do we get the same
(equivalent) result? Explain your answer. The result is different
because the formula is dependent on the symbols. The result is the
same because the formula is not dependent on the symbols. The
result is different because the formula is not dependent on the
symbols....

Use a scatterplot and the linear correlation coefficient r to
determine whether there is a correlation between the two variables.
Use alphaequals0.05. x 2 4 7 1 6 y 5 8 12 3 11 Click here to view a
table of critical values for the correlation coefficient.
LOADING... Does the given scatterplot suggest that there is a
linear correlation? A. Yes, because the data does not follow a
straight line. B. No, because the data follows a straight line. C....

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 25 minutes ago

asked 29 minutes ago

asked 39 minutes ago

asked 42 minutes ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago

asked 3 hours ago