Question

part 3 - determine and explain negative and positive associations
for each pair of variables, note whether you expect the association to be positive or negative, and explain why

scenario	positive or negative?	explanation
2. ( x = ) distance student travels to school <br> ( y = ) time spent traveling to school
3. ( x = ) ounces of insecticide used <br> ( y = ) mosquito population (hundreds per acre)	negative (handwritten)
4. ( x = ) hours a student spends watching tv <br> ( y = ) hours a student spends playing video games
5. ( x = ) hours spent studying the spelling of vocabulary words <br> ( y = ) number of vocabulary words spelled incorrectly	negative (handwritten)
6. ( x = ) hours spent digging a hole <br> ( y = ) depth of the hole (feet)	positive (handwritten)

Explanation:

To solve this, we analyze each variable pair for positive/negative association:

1. \( x \) = child’s age (years), \( y \) = child’s height (centimeters)

• Association: Positive
• Explanation: As a child’s age increases, their height typically increases (positive relationship).

2. \( x \) = distance from home to school, \( y \) = time spent to get to work

• Association: Positive
• Explanation: Greater distance from home to school (or work) usually means more time spent commuting (positive relationship).

3. \( x \) = ounces of insecticide used, \( y \) = mosquito population (hundreds per acre)

• Association: Negative
• Explanation: More insecticide kills more mosquitoes, so as \( x \) (insecticide) increases, \( y \) (mosquitoes) decreases (negative relationship).

4. \( x \) = hours a student spends watching TV, \( y \) = hours a student spends playing video games

• Association: Positive
• Explanation: Students who spend more time on TV often spend more time on other screen - based activities like video games (positive relationship).

5. \( x \) = hours spent studying spelling of vocabulary words, \( y \) = number of vocabulary words spelled incorrectly

• Association: Negative
• Explanation: More study time reduces spelling mistakes, so as \( x \) (study time) increases, \( y \) (incorrect spellings) decreases (negative relationship).

6. \( x \) = hours spent digging a hole, \( y \) = depth of the hole (feet)

• Association: Positive
• Explanation: More time spent digging usually results in a deeper hole, so as \( x \) (time) increases, \( y \) (depth) increases (positive relationship).

Final Answers (for each row’s “Explanation” column):

1. As age increases, height increases.
2. Greater distance means more commute time.
3. More insecticide reduces mosquitoes.
4. More TV time links to more video game time.
5. More study time reduces misspelled words.
6. More digging time increases hole depth.

Answer:

To solve this, we analyze each variable pair for positive/negative association:

1. \( x \) = child’s age (years), \( y \) = child’s height (centimeters)

• Association: Positive
• Explanation: As a child’s age increases, their height typically increases (positive relationship).

2. \( x \) = distance from home to school, \( y \) = time spent to get to work

• Association: Positive
• Explanation: Greater distance from home to school (or work) usually means more time spent commuting (positive relationship).

3. \( x \) = ounces of insecticide used, \( y \) = mosquito population (hundreds per acre)

• Association: Negative
• Explanation: More insecticide kills more mosquitoes, so as \( x \) (insecticide) increases, \( y \) (mosquitoes) decreases (negative relationship).

4. \( x \) = hours a student spends watching TV, \( y \) = hours a student spends playing video games

• Association: Positive
• Explanation: Students who spend more time on TV often spend more time on other screen - based activities like video games (positive relationship).

5. \( x \) = hours spent studying spelling of vocabulary words, \( y \) = number of vocabulary words spelled incorrectly

• Association: Negative
• Explanation: More study time reduces spelling mistakes, so as \( x \) (study time) increases, \( y \) (incorrect spellings) decreases (negative relationship).

6. \( x \) = hours spent digging a hole, \( y \) = depth of the hole (feet)

• Association: Positive
• Explanation: More time spent digging usually results in a deeper hole, so as \( x \) (time) increases, \( y \) (depth) increases (positive relationship).

Final Answers (for each row’s “Explanation” column):

1. As age increases, height increases.
2. Greater distance means more commute time.
3. More insecticide reduces mosquitoes.
4. More TV time links to more video game time.
5. More study time reduces misspelled words.
6. More digging time increases hole depth.