Classify the following attributes as binary, discrete, or continuous. Also classify them as qualitative (nominal or ordinal) or quantitative (interval or ratio). (a) Some cases may have more than one interpretation, so briefly indicate your reasoning if you think there may be some ambiguity. Example: Age in years. Answer: Discrete, quantitative, ratio Time in terms of AM or PM. Brightness as measured by a light meter. Brightness as measured by people's judgments. Angles as measured in degrees between 0 and 360. Bronze, Silver, and Gold medals as awarded at the Olympics. Height above sea level. Number of patients in a hospital. ISBN numbers for books. (Look up the format on the Web.) Ability to pass light in terms of the following values: opaque, translucent, transparent. Military rank. Distance from the center of campus. Density of a substance in grams per cubic centimeter. (b) Can you think of a situation in which identification numbers would be useful for prediction? (c) An educational psychologist wants to use association analysis to analyze test results. The test consists of 100 questions with four possible answers each. How would you convert this data into a form suitable for association analysis? In particular, what type of attributes would you have and how many of them are there?

(a)

1. Time in terms of AM or PM: Binary, qualitative, nominal (since there are only two options - AM or PM, and they don't have an order)
2. Brightness as measured by a light meter: Continuous, quantitative, ratio (since brightness can be measured on a continuous scale and has a true zero point)
3. Brightness as measured by people's judgments: Ordinal, qualitative (since people's judgments can be ranked but the differences between the ranks may not be equal)
4. Angles as measured in degrees between 0 and 360: Continuous, quantitative, interval (since angles can be measured on a continuous scale but there is no true zero point)
5. Bronze, Silver, and Gold medals as awarded at the Olympics: Ordinal, qualitative (since the medals can be ranked)
6. Height above sea level: Continuous, quantitative, ratio (since height can be measured on a continuous scale and has a true zero point)
7. Number of patients in a hospital: Discrete, quantitative, ratio (since the number of patients can be counted and has a true zero point)
8. ISBN numbers for books: Nominal, qualitative (since ISBN numbers are used for identification and don't have an order)
9. Ability to pass light in terms of the following values: opaque, translucent, transparent: Ordinal, qualitative (since these categories can be ranked)
10. Military rank: Ordinal, qualitative (since ranks can be ordered)
11. Distance from the center of campus: Continuous, quantitative, ratio (since distance can be measured on a continuous scale and has a true zero point)
12. Density of a substance in grams per cubic centimeter: Continuous, quantitative, ratio (since density can be measured on a continuous scale and has a true zero point)

(b) Identification numbers could be useful for prediction in a situation where they are not just random but contain some information about the characteristics of the entity they are assigned to. For example, in some countries, the first few digits of a person's social security number indicate the state where they were born. This could be used to predict the person's place of birth.

(c) For association analysis, the data should be converted into a binary format. Each question can be transformed into four binary attributes, one for each possible answer. The value of the attribute would be 1 if the student chose that answer and 0 otherwise. So, there would be a total of 400 (100*4) binary attributes.

(a)

1. Time in terms of AM or PM: Binary, qualitative, nominal (since there are only two options - AM or PM, and they don't have an order)
2. Brightness as measured by a light meter: Continuous, quantitative, ratio (since brightness can be measured on a continuous scale and has a true zero point)
3. Brightness as measured by people's judgments: Ordinal, qualitative (since people's judgments can be ranked but the differences between the ranks may not be equal)
4. Angles as measured in degrees between 0 and 360: Continuous, quantitative, interval (since angles can be measured on a continuous scale but there is no true zero point)
5. Bronze, Silver, and Gold medals as awarded at the Olympics: Ordinal, qualitative (since the medals can be ranked)
6. Height above sea level: Continuous, quantitative, ratio (since height can be measured on a continuous scale and has a true zero point)
7. Number of patients in a hospital: Discrete, quantitative, ratio (since the number of patients can be counted and has a true zero point)
8. ISBN numbers for books: Nominal, qualitative (since ISBN numbers are used for identification and don't have an order)
9. Ability to pass light in terms of the following values: opaque, translucent, transparent: Ordinal, qualitative (since these categories can be ranked)
10. Military rank: Ordinal, qualitative (since ranks can be ordered)
11. Distance from the center of campus: Continuous, quantitative, ratio (since distance can be measured on a continuous scale and has a true zero point)
12. Density of a substance in grams per cubic centimeter: Continuous, quantitative, ratio (since density can be measured on a continuous scale and has a true zero point)

(b) Identification numbers could be useful for prediction in a situation where they are not just random but contain some information about the characteristics of the entity they are assigned to. For example, in some countries, social security numbers can tell you the state in which the person was born or the year they were born.

(c) For association analysis, the data should be converted into a binary format. Each question can be represented as four binary attributes (one for each possible answer), indicating whether the student chose that answer or not. So, there would be a total of 400 binary attributes.