Question

In: Statistics and Probability

1). Use the data given below to answer the following questions Observation Height (X1) Weight (X2)...

1). Use the data given below to answer the following questions

Observation Height (X1) Weight (X2)
1 69 153
2 69 175
3 68 155
4 65 150
5 72 143
6 62 140
7 66 132
8 65 130
9 76 145
10 63 145

i) Evaluate the sample covariance for the height and weight

ii) Find the sample correlation of the two variables.

Solutions

Expert Solution

(i)

X                  Y                XY              X2                      Y2

69               153              10557         4761                23409

69               175              12075           4761             30625

68              155                10540            4624            24025

65              150               9750              4225             22500

72              143               10296            5184              20449

62              140              8680               3844               19600

66              132              8712               4356               17424

65              130            8450                 4225               16900

76              145            11020               5776                21025

63                145           9135               3969                21025

--------------------------------------------------------------------------------------------

675             1468         99215                45725               216982

n = 10

So,

Covariance (X,Y) = pXY is given by:

So,

pXY = 125.001/9 = 13.889

So,

Sample Covariance = 13.889

(ii)

X                  Y                XY              X2                      Y2

69               153              10557         4761                23409

69               175              12075           4761             30625

68              155                10540            4624            24025

65              150               9750              4225             22500

72              143               10296            5184              20449

62              140              8680               3844               19600

66              132              8712               4356               17424

65              130            8450                 4225               16900

76              145            11020               5776                21025

63                145           9135               3969                21025

--------------------------------------------------------------------------------------------

675             1468         99215                45725               216982

So,

Sample correlation = 0.2549

orchestra answered 2 years ago
Next > < Previous

Related Solutions

Height vs Weight - Erroneous Data: You will need to use software to answer these questions....
Height vs Weight - Erroneous Data: You will need to use software to answer these questions. Below is the scatterplot and corresponding data for the height and weight of 11 randomly selected adults. You should notice something odd about the last entry.           index height (x) weight (y) inches pounds 1 60 120 2 72 200 3 65 130 4 71 205 5 67 180 6 70 180 7 69 193 8 71 195 9 63 115 10 62 140...
Height vs Weight - Erroneous Data: You will need to use software to answer these questions....
Height vs Weight - Erroneous Data: You will need to use software to answer these questions. Below is the scatterplot, regression line, and corresponding data for the height and weight of 11 randomly selected adults. You should notice something odd about the last entry.           index height (x) weight (y) inches pounds 1 60 120 2 72 200 3 65 130 4 71 205 5 69 180 6 68 180 7 69 193 8 69 195 9 63 115 10...
Use the following data to answer the questions below:
Use the following data to answer the questions below:             Q                 VC             MC           AVC              1                 $10              ___            ___                                   2                16              ___            ___                       3                20              ___            ___                                   4                25              ___            ___              5                31              ___            ___              6                  38              ___            ___                  7                  46              ___            ___8                  55              ___            ___9                  65              ___            ___         a. Calculate the marginal cost and average variable cost for each level of production.b. How much would the firm produce if it could sell its product for...
1.) Use the given information below to answer the following questions. a.) A sample of 25...
1.) Use the given information below to answer the following questions. a.) A sample of 25 lightbulbs was taken and it was found that the mean lifetime of a certain bulb for a movie projector is 520 hours with a standard deviation of 50 hours. The standing assumption of the manufacturing company is that the lifetime of this type pf bulb is no more than 500 hours. Assume a normal distribution. Does the data support the company’s claim at a...
Use the following information to answer the questions below. Observation Price Quantity A $1.00 20 B...
Use the following information to answer the questions below. Observation Price Quantity A $1.00 20 B $2.00 15 1. Calculate a price elasticity of demand. You must show all your work to earn credit. 2. Given the elasticity of demand, a 10% increase in price will cause quantity demanded to fall by what percentage? Explain your answer. 3. Is this demand elastic or inelastic? Explain your answer. Part II Walmart advertises that it has rolled back prices. If Walmart is...
If the joint probability distribution of X1 and X2 is given by: f(X1, X2) = (X1*X2)/36...
If the joint probability distribution of X1 and X2 is given by: f(X1, X2) = (X1*X2)/36 for X1 = 1, 2, 3 and X2 = 1, 2, 3, find the joint probability distribution of X1*X2 and the joint probability distribution of X1/X2.
Use the data given in the table to answer the following questions. The data represents the...
Use the data given in the table to answer the following questions. The data represents the average number of miles that a salesperson travels in a day verses the number of sales made each month. Miles, x 24 32 75 41 76 107 32 46 112 Sales, y 76 58 190 112 141 235 24 147 188 (a) What is the value of the correlation coefficient for this set of data? Round to 3 decimal places. (b) What is the...
Given the data set below, use it to answer the following questions: 10, 20, 30, 40,...
Given the data set below, use it to answer the following questions: 10, 20, 30, 40, 50 a. Find the standard deviation b. Add 5 to each data set value and find the standard deviation. c. Subtract 5 from each value and find the standard deviation. d. Multiply by 5 on each value and find the standard deviation. e. Divide by 5 on each value and find the standard deviation. f. Generalize the results in parts a-e.
The production function of a competitive firm is given by f(x1, x2) = x1^1/3 (x2 −...
The production function of a competitive firm is given by f(x1, x2) = x1^1/3 (x2 − 1)^1/3 The prices of inputs are w1 = w2 = 1. (a) Compute the firm’s cost function c(y). (b) Compute the marginal and the average cost functions of the firm. (c) Compute the firm’s supply S(p). What is the smallest price at which the firm will produce? 2 (d) Suppose that in the short run, factor 2 is fixed at ¯x2 = 28. Compute...
Please answer all the questions. Thank you Use the following data to answer the questions below:...
Please answer all the questions. Thank you Use the following data to answer the questions below: Column 1 Column 2 Column 3 Y in $ C in $ 0 500 500 850 1,000 1,200 1,500 1,550 2,000 1,900 2,500 2,250 3,000 2,600 What is mpc and mps? Compute mpc and mps. Assume investment equals $ 100, government spending equals $ 75, exports equal $ 50 and imports equal $ 35. Compute the aggregate expenditure in column 3. Draw a graph...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT