Suppose the following data set contains the monthly adjusted stock prices for technology company A, and a consumer-goods company B from 2013–2018. Copy and paste the data into Excel and use the Excel functions for covariance and correlation to solve the question. Date A B 6/1/2013 46.44 67.71 7/1/2013 52.71 70.54 8/1/2013 56.60 68.98 9/1/2013 59.00 67.00 10/1/2013 63.40 71.44 11/1/2013 67.32 74.99 12/1/2013 70.69 72.55 1/1/2014 63.29 68.40 2/1/2014 66.43 70.68 3/1/2014 70.57 72.38 4/1/2014 77.39 74.08 5/1/2014 82.87 73.11 6/1/2014 88.47 71.17 7/1/2014 90.95 69.05 8/1/2014 97.37 75.73 9/1/2014 96.21 76.29 10/1/2014 102.99 79.42 11/1/2014 113.21 82.84 12/1/2014 105.66 83.43 1/1/2015 112.03 77.35 2/1/2015 122.64 78.64 3/1/2015 119.32 75.77 4/1/2015 120.00 73.58 5/1/2015 124.84 73.14 6/1/2015 120.76 73.01 7/1/2015 116.85 71.61 8/1/2015 108.91 66.66 9/1/2015 106.91 67.82 10/1/2015 115.66 71.89 11/1/2015 114.51 71.09 12/1/2015 102.54 75.31 1/1/2016 94.98 77.42 2/1/2016 94.35 76.77 3/1/2016 106.67 78.65 4/1/2016 91.02 76.61 5/1/2016 97.90 78.09 6/1/2016 94.37 81.49 7/1/2016 102.69 81.36 8/1/2016 104.51 84.62 9/1/2016 111.82 86.92 10/1/2016 112.30 84.13 11/1/2016 109.36 80.63 12/1/2016 115.09 82.17 1/1/2017 120.49 85.53 2/1/2017 135.76 89.53 3/1/2017 142.88 88.35 4/1/2017 142.87 85.93 5/1/2017 151.80 85.31 6/1/2017 143.82 86.40 7/1/2017 148.45 90.95 8/1/2017 163.49 92.06 9/1/2017 154.36 89.80 10/1/2017 169.11 84.27 11/1/2017 172.88 87.49 12/1/2017 169.90 92.35 1/1/2018 168.11 86.90 2/1/2018 178.72 76.80 3/1/2018 169.14 77.55 4/1/2018 166.63 75.68 5/1/2018 189.86 86.31 (c) Compute the sample covariance. (Round your answer to two decimal places.) Interpret the sample covariance. 1. There is a positive relationship between the two variables. 2. There is a negative relationship between the two variables. 3. There is no relationship between the two variables. (d) Compute the sample correlation coefficient. (Round your answer to two decimal places.) What does this value indicate about the relationship between the stock price of company A and the stock price of company B? 1. There is a moderately strong positive relationship between the two variables. 2. There is a moderately strong negative relationship between the two variables. 3. There is no relationship between the two variables. 4. There is a positive relationship between the two variables, but the strength of this relationship cannot be determined based on the sample correlation coefficient. 5. There is a negative relationship between the two variables, but the strength of this relationship cannot be determined based on the sample correlation coefficient.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Suppose the following data set contains the monthly adjusted stock prices for technology company A, and a consumer-goods company B from 2013–2018. Copy and paste the data into Excel and use the Excel
Date | A | B |
6/1/2013 | 46.44 | 67.71 |
7/1/2013 | 52.71 | 70.54 |
8/1/2013 | 56.60 | 68.98 |
9/1/2013 | 59.00 | 67.00 |
10/1/2013 | 63.40 | 71.44 |
11/1/2013 | 67.32 | 74.99 |
12/1/2013 | 70.69 | 72.55 |
1/1/2014 | 63.29 | 68.40 |
2/1/2014 | 66.43 | 70.68 |
3/1/2014 | 70.57 | 72.38 |
4/1/2014 | 77.39 | 74.08 |
5/1/2014 | 82.87 | 73.11 |
6/1/2014 | 88.47 | 71.17 |
7/1/2014 | 90.95 | 69.05 |
8/1/2014 | 97.37 | 75.73 |
9/1/2014 | 96.21 | 76.29 |
10/1/2014 | 102.99 | 79.42 |
11/1/2014 | 113.21 | 82.84 |
12/1/2014 | 105.66 | 83.43 |
1/1/2015 | 112.03 | 77.35 |
2/1/2015 | 122.64 | 78.64 |
3/1/2015 | 119.32 | 75.77 |
4/1/2015 | 120.00 | 73.58 |
5/1/2015 | 124.84 | 73.14 |
6/1/2015 | 120.76 | 73.01 |
7/1/2015 | 116.85 | 71.61 |
8/1/2015 | 108.91 | 66.66 |
9/1/2015 | 106.91 | 67.82 |
10/1/2015 | 115.66 | 71.89 |
11/1/2015 | 114.51 | 71.09 |
12/1/2015 | 102.54 | 75.31 |
1/1/2016 | 94.98 | 77.42 |
2/1/2016 | 94.35 | 76.77 |
3/1/2016 | 106.67 | 78.65 |
4/1/2016 | 91.02 | 76.61 |
5/1/2016 | 97.90 | 78.09 |
6/1/2016 | 94.37 | 81.49 |
7/1/2016 | 102.69 | 81.36 |
8/1/2016 | 104.51 | 84.62 |
9/1/2016 | 111.82 | 86.92 |
10/1/2016 | 112.30 | 84.13 |
11/1/2016 | 109.36 | 80.63 |
12/1/2016 | 115.09 | 82.17 |
1/1/2017 | 120.49 | 85.53 |
2/1/2017 | 135.76 | 89.53 |
3/1/2017 | 142.88 | 88.35 |
4/1/2017 | 142.87 | 85.93 |
5/1/2017 | 151.80 | 85.31 |
6/1/2017 | 143.82 | 86.40 |
7/1/2017 | 148.45 | 90.95 |
8/1/2017 | 163.49 | 92.06 |
9/1/2017 | 154.36 | 89.80 |
10/1/2017 | 169.11 | 84.27 |
11/1/2017 | 172.88 | 87.49 |
12/1/2017 | 169.90 | 92.35 |
1/1/2018 | 168.11 | 86.90 |
2/1/2018 | 178.72 | 76.80 |
3/1/2018 | 169.14 | 77.55 |
4/1/2018 | 166.63 | 75.68 |
5/1/2018 | 189.86 | 86.31 |
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