This exercise asks you to perform an SPSS dataset from the data provided below.

It shows the temperature of water in a tea cup over time.The times are in minutes, the temperatures a Fahrenheit (no, I do NOT boil my water to 195C!). "Time_period" is 1 for the first 30 minutes, 2 thereafter.

Change_Level is 2 = large change, 1 = small change, -9 = Not applicable (to be treated as missing data).

Generate an SPSS data file. Be sure to put in value labels for the two dichotomous variables. And be sure to handle the -9 correctly.

Time	Time_Period	Temperature	Change_Level
1	1	196	-9
5	1	176	2
10	1	160	2
15	1	149	2
20	1	140	2
25	1	133	2
30	1	127	1
35	2	122	1
40	2	118	1
45	2	113	1
50	2	110	1
55	2	107	1
60	2	104	1
65	2	101	1
70	2	99	1
75	2	97	1

1. To check that the data was entered correctly, please provide the Pearson correlation between time and temperature. Here are some choices. You should get one of these exactly. If you don't, double check your data.

A. -0.993

B. -0.976

C. -0.960

D. -0.955

E. -0.940

F. -0.934

2. What p-value does SPSS report for the Pearson correlation?

3. What do you conclude?

A. There is good evidence for a correlation not equal to 0.

B. There is good evidence for a correlation greater than 0.5 or less than -0.5.

C. There is good evidence for a correlation of greater magnitude than the observed correlation (from Q 1).

D. The p-value is so small that the correlation is not significant.

E. The correlation is estimated with a very high precision as defined by the p-value.

4. Using linear regression, predict the temperature of the water at 23.09 minutes. Round your answer to the nearest whole number.

5. The change in temperature from time to time is not a function only of the temperature itself, but also of the surrounding temperature, which is about 75.

Generate a new variable that is the water temperature minus 75. Then take the logarithm in base 10 of that difference. If you did this correctly, the mean should be 1.6695.

Obtain the Pearson correlation between time and the log variable you just created. What is it? Keep at least 3 significant digits as this correlation is rather close to -1 .

6. Obtain the Spearman correlation between time and temperature. Why was Spearman that value?

A. The Spearman correlation is an approximation to the Pearson.

B. The Spearman correlation looks at the order of the two variables, which in this case is perfectly reversed for temperature and time.

C. There is no way to explain the exact value, but based on the pattern, it should be negative.

D. The Spearman correlation always takes on the values 1, 0.5, 0, -0.5, or -1 since the rank method makes other values impossible.

E. We need the p-value to explain the correlation.

7. Based on a simple linear model, determine the proportion of temperature that is associated with time. Keep 4 digits like 0.6543.

8. Let's test if the linear model is ideal for this data. Generate a variable called Time_2 that is the time variable squared.Then conduct multiple linear regression predicting temperature from time and Time_2. Does Time_2 add to the model?

A. No, the regression weight for it is very small compared to time.

B. Yes, the standardized regression weight is substantial.

C. No, the p-value is non-significant.

D. Yes, the p-value is quite small and significant.

E. A and C

F. B and D

9. You can calculate the proportion of additional variance accounted for by adding Time_2. To perform this, take the adjusted r² provided by SPSS and subtract from it the r² from a single predictor that you did earlier.What do you get? Use 4 digits, like 0.0778

10.Obtain a crosstabulation of time_period (row variable) and change_level (column). Include row percentages. Does the crosstabulation indicate an association between the two? If so, how?

A. No, the row total percentages are 100% for each time period.

B. No. About 2/3 (66.7%) are small change level, and 33.3% large change level, as would be expected.

C. No. The row percentages shown are determined by the counts (for example, 5/6 - 83.3%) thus showing the absence of any pattern.

D. Yes, 83.3% of the first 30 time group is large change, and only 16.7% is not.

E. Yes. 9 of the later time period are small changes versus only 1 of the first 30.

F. Yes. 83.3% of the first 30 are large changes versus 0% of the later time period.