Task 2

Use Tornados data and find two months (month X and month Y) for which we have the SECOND strongest NEGATIVE correlation. Create the chart where x-axis and y-axis represent the tornadoes for month X and month Y. (Choose the months in chronological order X comes before Y) Properly label the chart and be sure that you have the fitted line as well as R2 and answer questions 1 to 4.

1. Which of the following statement is true?

• a. The observed positive trend means that if we observe more tornadoes for month X we will also see more tornadoes for month Y.
• b. The observed positive trend means that as years go by we see more and more tornadoes.
• c. The observed negative trend means that if we observe less numbers of tornadoes for month X we will see less tornadoes for month Y.
• d. The observed negative trend means that as years go by we see less and less tornadoes.
• e. None of the choices.

2. If month X has 50 tornadoes what is the prediction for month Y? (give the closest number using the line equation)

• a. 22.213 tornadoes observed in month Y if month X has 50 tornadoes
• b. 80.05 tornadoes observed in month Y if month X has 50 tornadoes
• c. 17.7 tornadoes observed in month Y if month X has 50 tornadoes.
• d. 117.15 tornadoes observed in month Y if month X has 50 tornadoes
• e. None of the choices.

3. Based on this analysis, would you say that this prediction is very reliable, somewhat reliable or not reliable and why?

• a. not very reliable prediction because R-square is small and data on the chart looks very random. Correlation = -0.13 is rather weak so the number of tornadoes in month X is not a good predictor of the number of tornadoes in month Y.
• b. not reliable prediction because R-square=0.0498 is small and data on the chart looks very random. Correlation=-0.223 is weak so the number of tornadoes in month X is not a good predictor of the number of tornadoes in month Y.
• c. somewhat reliable prediction because R-square=0.0498 is decent and data on the chart looks very random. Correlation=-0.223 is moderate so the number of tornadoes in month X is a good predictor of the number of tornadoes in month Y.
• d. somewhat reliable prediction because R-square =0.0159 is decent and data on the chart looks very random. Correlation=-0.13 is moderate so the number of tornadoes in month X is a good predictor of the number of tornadoes in month Y.
• e. None of the choices.

4. What are the months X and Y?

• a. February and April
• b. August and December
• c. July and August
• d. None of these

Homework 5 / Task 2

Task 1 Task 3

Upload US crime data and compare the burglary counts for the states of Hawaii, California, Arizonaand Nevada. Your job is to identify which of the three states is most correlated to California. Make scattered plot chart with X representing California and Y representing that state in question, plot the line and compute the R-square. Answer questions 5 to 8:

5. What are the approximate slope and the R-squares on your chart?)

• a. Slope=0.048 and R-square=0.9086
• b. Slope=18.841 and R-square=0.9086
• c. Slope=0.0287 and R-square=0.7959
• d. Slope=27.753 and R-square=0.7959

6. Interpret the slope based on the chart.

• a. One expects 0.0287 burglaries in Hawaii when there are no burglaries in California.
• b. For 100 additional burglaries in California one expects to see an increase of about 3 burglaries in Hawaii.
• c. For one additional burglary in Hawaii one expects to see an increase of about 19 burglaries in California.
• d. For 100 additional burglaries in California one expects to see an increase of about 5 burglaries in Hawaii
• e. For one additional burglary in Hawaii one expects to see an increase of about 28 burglaries in California.

7. What is the approximate Y-intercept and what is its statistical interpretation?

• a. Y-intercept=18607. It is the predicted number of burglary in California when there are no burglaries in Hawaii
• b. Y-intercept=0.0287. It is the predicted number of burglary in Hawaii when there are no burglaries in California
• c. Y-intercept=27.753. For one additional burglary in Hawaii one expects to see an increase of about 28 burglaries in California
• d. Y-intercept= 1912.4. It is the predicted number of burglary in Hawaii when there are no burglaries in California

8. The highest dot on your chart has (approximately) the following X-coordinate.

• a. 17822
• b. 545138
• c. 540806
• d. 16726

Homework 5 / Task 3

Open House_Price5variables data. Create scatter plot chart with X representing the age of the house and Y representing the selling price of the house in $100,000; plot the line and compute the R-square. Answer questions 9 to 12:

9. What are the slope and the R-squares on your chart?

• a. Slope= -1.6019, R-square=0.1175
• b. Slope=-0.0734, R-square=0.1175
• c. Slope=9.8861, R-square=0.1175
• d. Slope=47.89, R-square=0.1175

10. What is the Y-intercept and its interpretation based on the chart?

• a. Y-intercept=9.8861, it is the predicted selling price of a brand new house (zero year-old house) in $100,000.
• b. Y-intercept=47.89, it is the predicted selling price of a brand new house (zero year-old house) in $100,000.
• c. Y-intercept=9.8861, for one additional year one expects to see a decrease of about 9.8861 hundred thousand dollars in the selling price of the house.
• d. Y-intercept=47.89, for one additional year one expects to see a decrease of about 47.89 hundred thousand dollars in the selling price of the house.

11. If a house is 7 years old, using the chart and the equation, what is your prediction of the house's selling price? Pick the closest answer.

• a. $ 3,667,670.00
• b. $ 937,230.00
• c. $ 1,039,990.00
• d. $ 5,910,330.00

12. What does each dot represent?

• a. The Selling Price of a house
• b. The Age of a house
• c. A House
• d. The housing market

Homework 5 / Task 4

Task 3 Task 5

Open the data Cars04-HW6&5 and answer questions 13 to 14.

13. Compute the Average, Median, and Standard Deviation Horsepower column. Which of the following statement is true?

• a. Median < Average < Standard deviation
• b. Average < Standard deviation
• c. Standard deviation
• d. Average < Median < Standard deviation
• e. Standard Deviation < Average < Median

14. Using 2-standard deviation rule of thumb and the information you obtained from question 13 which of the following is true? Round the numbers to nearest integer. (4 points)

• a. 90% of data are between 72 and 328
• b. 95% of data are between 72 and 328
• c. 95% of data are between 136 and 264
• d. 65% of data are between 72 and 327
• e. None of these

Homework 5 / Task 5

Task 4 Task 6

Upload Cars04-HW6&5 data and check which pair among the following five categories Cylinder, Horsepower, CityMPG, Weight, RetailPrice has the highest correlation. Pick those two categories and make a scattered plot chart. For X coordinate, out of these two categories, choose the one that come first alphabetically. (Example: if you choose Cylinder and Horsepower then Cylinder should be X Coordinate). Plot the line and compute the R-square. Answer the questions 15 to 17.

15. What category did you choose for X? (4 points)

• a. Cylinder
• b. Horsepower
• c. City MPG
• d. Weight
• e. Retail Price

16. According to the convention table how would you describe the strength of the relation between X and Y coordinates?

From 0.0 to 0.2

Poor

From 0.2 to 0.4

Decent

From 0.4 to 0.6

Good

From 0.6 to 0.85

Very Good

From 0.85 to 1.0

Excellent

a. Poor

• b. Decent
• c. Good
• d. Very Good
• e. Excellent

17. What does each dot represents?

• a. A car brand
• b. A car price
• c. A car
• d. None of these

Task 4

Homework 5 / Task 6

Task 5 Task 7

Two dice were rolled. Answer questions 18 to 20:

18. What is the probability that the first die will have "a natural number greater than 1 which can only be divisible by 1 and itself"?

• a. 2/6
• b. 3/6
• c. 4/6
• d. 5/6

19. What is the probability that one die has number "5" as the outcome and the other die has number "1" as the outcome?

• a. 1/36
• b. 1/12
• c. 1/18
• d. 2/72
• e. 1/7

20. What is the probability that the second die will have " a number that is less than the number on the first die "?

• a. 13/36
• b. 15/36
• c. 20/36
• d. 21/36

Homework 5 / Task 7

Four coins were tosses. Answer questions 21 to 24:

21. What is the probability that the second coin has a "Tail" as outcome?

• a. 1/4
• b. 1/3
• c. 1/2
• d. 1/8
• e. None of these

22. What is the probability that the number of "HEADs" on these four coins is equal to 3?

• a. 1/4
• b. 1/16
• c. 1/8
• d. 1/36
• e. None of these

23. What is the probability that the second coin has "HEAD" and the third coin has "TAIL" as outcomes?

• a. 1/36
• b. 1/8
• c. 1/16
• d. 1/4
• e. None of these

24. What is the probability that the first and last coins have "Heads"? (4 points)

• a. 3/16
• b. 4/16
• c. 5/16
• d. 3/8

Homework 5 / Task 8

Task 7

25. If a person picks a pair of different Months, what is the probability that both months (different) have less than 31 days? Hint: Use the tornados data to create a correlation matrix to get the possible combinations. (4 points)

• a. 5/66
• b. 10/66
• c. 11/66
• d. 14/66