Question

1. association suppose you were to collect data for each pair of variables. you want to make a scatterplot. which variable would you use as the explanatory variable and which as the response variable? why? what would you expect to see in the scatter - plot? discuss the likely direction, form, and strength.

a) apples: weight in grams, weight in ounces
b) for each week: ice - cream cone sales, air - conditioner sales
c) college freshmen: shoe size, grade - point average
d) gasoline: number of miles you drove since filling up, gallons remaining in your tank

1. association suppose you were to collect data for each pair of variables. you want to make a scatterplot. which variable would you use as the explanatory variable and which as the response variable? why? what would you expect to see in the scatter - plot? discuss the likely direction, form, and strength.

a) cell phone data plans: file size, cost
b) lightning strikes: distance from lightning, time delay of the thunder
c) a streetlight: its apparent brightness, your distance from it
d) cars: weight of car, age of owner

1. scatterplots which of the four scatterplots show

a) little or no association?
b) a negative association?
c) a linear association?
d) a moderately strong association?
e) a very strong association?

Explanation:

1a)

The weight of apples in grams is likely the explanatory variable as it is an independent - like property, and weight in ounces is the response variable since it depends on the gram - weight conversion. The direction is positive (as gram - weight increases, ounce - weight increases), the form is linear (due to the fixed conversion factor), and the strength is very strong (exact linear relationship based on conversion).

1b)

The week number could be the explanatory variable as it is an independent time - based variable. Ice cream cone sales and air - conditioner sales are response variables. The direction is positive for both as in summer (higher week numbers in summer), both sales are likely to increase. The form may be seasonal (peaks in summer), and the strength is moderately strong as they are related to warm weather.

1c)

It's hard to determine a clear explanatory and response variable here. There is likely no relationship, so no clear direction, form, or strength.

1d)

The number of miles driven since filling up is the explanatory variable as it is an independent action. Gallons remaining in the tank is the response variable. The direction is negative (as miles driven increase, gallons remaining decrease), the form is likely linear (assuming constant fuel consumption), and the strength is strong if fuel consumption is consistent.

2a)

The file size could be the explanatory variable as it determines the cost in a cell - phone data plan. The cost is the response variable. The direction is positive (higher file size, higher cost), the form is likely linear (based on data - plan rates), and the strength is strong.

2b)

The distance from lightning is the explanatory variable as it is an independent factor. The time delay of the thunder is the response variable. The direction is positive (as distance increases, time delay increases), the form is linear (speed of sound is constant), and the strength is very strong.

2c)

The distance from the streetlight is the explanatory variable. The apparent brightness is the response variable. The direction is negative (as distance increases, brightness decreases), the form is an inverse - square relationship (physics principle), and the strength is very strong.

2d)

There is likely no relationship between the weight of a car and the age of the owner, so no clear explanatory/response variable, direction, form, or strength.

3a)

Plot (2) shows little or no association as the points are scattered randomly.

3b)

Plot (1) shows a negative association as the points generally trend downwards from left to right.

3c)

Plot (1) shows a linear association as the points follow a somewhat straight - line pattern.

3d)

Plot (1) shows a moderately strong association as the points are somewhat clustered around an imaginary line.

3e)

Plot (1) if the relationship is very consistent, or if there is a better - fitting plot not shown, could show a very strong association.

Answer:

1a) Explanatory: Weight in grams; Response: Weight in ounces. Positive direction, linear form, very strong strength.
1b) Explanatory: Week number; Responses: Ice - cream cone sales, air - conditioner sales. Positive direction, seasonal form, moderately strong strength.
1c) No clear explanatory/response, no direction, form, or strength.
1d) Explanatory: Number of miles driven since filling up; Response: Gallons remaining in the tank. Negative direction, linear form, strong strength.
2a) Explanatory: File size; Response: Cost. Positive direction, linear form, strong strength.
2b) Explanatory: Distance from lightning; Response: Time delay of thunder. Positive direction, linear form, very strong strength.
2c) Explanatory: Distance from streetlight; Response: Apparent brightness. Negative direction, inverse - square form, very strong strength.
2d) No clear explanatory/response, no direction, form, or strength.
3a) Plot (2)
3b) Plot (1)
3c) Plot (1)
3d) Plot (1)
3e) Plot (1)