Question

1. coral reefs and cell phones identify the explanatory variable and the response variable for the following relationships, if possible. explain your reasoning

(a) the weight gain of corals in aquariums where the water temperature is controlled at different levels
(b) the number of text messages sent and the number of phone calls made in a sample of 100 students

1. teenagers and corn yield identify the explanatory variable and the response variable for the following relationships, if possible. explain your reasoning.

(a) the height and arm span of a sample of 50 teenagers
(b) the yield of corn in bushels per acre and the amount of rain in the growing season

1. heavy backpacks ninth - grade students at the webb schools go on a backpacking trip each fall. students are divided into hiking groups of size 8 by selecting names from a hat. before leaving, students and their backpacks are weighed. the data here are from one hiking group. make a scatterplot by hand that shows how backpack weight relates to body weight.

body weight (lb) 120 187 109 103 131 165 158 116
backpack weight (lb) 26 30 26 24 29 35 31 28

1. putting success how well do professional golfers putt from various distances to the hole? the data show various distances to the hole (in feet) and the percent of putts made at each distance for a sample of golfers. make a scatterplot by hand that shows how the percent of putts made relates to the distance of the putt.

distance (ft) percent made distance (ft) percent made
2 93.3 12 25.7
3 83.1 13 24.0
4 74.1 14 31.0
5 58.9 15 16.8
6 54.8 16 13.4
7 53.1 17 15.9
8 46.3 18 17.3
9 31.8 19 13.6
10 33.5 20 15.8

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3. more putting s exercise 4. des from hole and p professional gol
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Explanation:

Problem 1 (a)

Step1: Define Variables

Explanatory variable: Water temperature (we control/change it to see effect on coral weight gain).
Response variable: Weight gain of corals (it responds to changes in water temperature).
Reasoning: Water temperature is manipulated (different levels), so it explains changes in coral weight gain.

Step1: Define Variables (for 1b)

Explanatory variable: Not clear (no obvious causal direction between text messages and phone calls; they may be associated but neither clearly explains the other).
Response variable: Not clear (same reason as above).
Reasoning: Both are behaviors of students; no clear cause - effect (e.g., sending texts doesn't necessarily cause phone calls or vice versa).

Problem 2 (a)

Step1: Define Variables

Explanatory variable: Not clear (height and arm span are related but neither is clearly explanatory; they are both physical measurements with a correlation, not a clear cause - effect).
Response variable: Not clear (same as above).
Reasoning: In teenagers, height and arm span are associated (biologically related), but neither is manipulated to cause the other.

Step1: Define Variables (for 2b)

Explanatory variable: Amount of rain (it can influence corn growth and yield).
Response variable: Yield of corn (it responds to the amount of rain during the growing season).
Reasoning: Rain is an environmental factor that affects corn production, so it explains changes in corn yield.

Problem 3: Making a Scatterplot

Step1: Identify Axes

• X - axis: Body weight (lb) (explanatory variable, values: 120, 187, 109, 103, 131, 165, 158, 116).
• Y - axis: Backpack weight (lb) (response variable, values: 26, 30, 26, 24, 29, 35, 31, 28).

Step2: Plot Points

For each pair \((\text{Body Weight}, \text{Backpack Weight})\):

• \((120, 26)\), \((187, 30)\), \((109, 26)\), \((103, 24)\), \((131, 29)\), \((165, 35)\), \((158, 31)\), \((116, 28)\).

Mark these points on a graph with appropriate scales (e.g., X - axis from 100 - 200, Y - axis from 20 - 40).

Problem 4: Making a Scatterplot

Step1: Identify Axes

• X - axis: Distance (ft) (explanatory variable, values: 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20).
• Y - axis: Percent made (response variable, values: 93.3, 83.1, 74.1, 58.9, 54.8, 53.1, 46.3, 31.8, 33.5, 25.7, 24.0, 31.0, 16.8, 13.4, 15.9, 17.3, 13.6, 15.8).

Step2: Plot Points

For each pair \((\text{Distance}, \text{Percent made})\), mark the points on a graph (e.g., X - axis from 0 - 25, Y - axis from 0 - 100) to show the relationship between putt distance and success rate.

Answer:

s (Summarized for Each Part):

1. (a) Explanatory: Water temperature; Response: Coral weight gain.

(b) No clear explanatory/response (no causal direction).

1. (a) No clear explanatory/response (correlated, not causal).

(b) Explanatory: Amount of rain; Response: Corn yield.

1. Scatterplot with body weight on X, backpack weight on Y, points as listed.
2. Scatterplot with distance on X, percent made on Y, points as listed.