Math / Data & Statistics

Question2 Multiple Choice 1 point slope of the regression line?
1. The cost of flood insurance increases by $\$ 500$ for every foot of elevation increase II. The cost of flood insurance is $\$ 10,000$ regarders of elevation III. The cost of flood insurance decreases by $\$ 500$ for every foot of elevation increase II only Neither 1, nor II, nor III I only III only 3 True or False 1 point
If, on average, $y$ increase as $x$ increase, the comrelation coefficient is positive. True False 4 Multiple Choice 1 point
Which of the following are reasons why observations with $r$ values close to 1 cannot be used to establish causality? The relationship between variables could be negative. The observations mary not include a sufficient number of samples. The relationship between variables may be nonlinear. An unidentified third variable corld be influencing both variables under investigation.

Studdy Solution

STEP 1

What is this asking? We've got a mix of questions here!
One's about how flood insurance cost changes with elevation, another checks if we understand what a positive correlation means, and the last one asks why a strong correlation doesn't always mean one thing causes another. Watch out! Don't mix up correlation and causation!
Just because two things happen together doesn't mean one causes the other.
Also, remember that correlation is about linear relationships.

STEP 2

1. Flood Insurance and Elevation
2. Positive Correlation
3. Correlation vs.
Causation

STEP 3

Alright, let's break down these flood insurance scenarios!
The first one says the cost goes up by $\$500$ for every foot higher the elevation.
That means a positive relationship between elevation and cost.

STEP 4

The second scenario says the cost is always $\$10,000$ , no matter the elevation.
That means there's no relationship between elevation and cost.

STEP 5

The third scenario says the cost goes down by $\$500$ for every foot higher the elevation.
That means a negative relationship between elevation and cost.

STEP 6

The problem implies a linear relationship between elevation and cost, and asks about the slope.
Only scenario I describes a positive slope (cost increase per foot).

STEP 7

Remember, a positive correlation means that as one variable ( $x$ ) increases, the other variable ( $y$ ) tends to increase too.
They move in the same direction!

STEP 8

So, if on average, $y$ increases as $x$ increases, then yes, the correlation coefficient is positive.
It's true!

STEP 9

Even if we have a correlation coefficient ( $r$ ) close to 1 (a strong positive correlation) or close to -1 (a strong negative correlation), it doesn't prove that one variable causes the other to change.

STEP 10

A strong correlation just means they move together, not that one makes the other move.
There could be a third hidden variable influencing both of them!
That's why the answer is "An unidentified third variable could be influencing both variables under investigation."

STEP 11

1. I only
2. True
3. An unidentified third variable could be influencing both variables under investigation.

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Studdy Solution

STEP 1

STEP 2

1. Flood Insurance and Elevation
2. Positive Correlation
3. Correlation vs.
Causation

STEP 3

Alright, let's break down these flood insurance scenarios!
The first one says the cost goes up by $\$500$ for every foot higher the elevation.
That means a positive relationship between elevation and cost.

STEP 4

The second scenario says the cost is always $\$10,000$ , no matter the elevation.
That means there's no relationship between elevation and cost.

STEP 5

The third scenario says the cost goes down by $\$500$ for every foot higher the elevation.
That means a negative relationship between elevation and cost.

STEP 6

The problem implies a linear relationship between elevation and cost, and asks about the slope.
Only scenario I describes a positive slope (cost increase per foot).

STEP 7

Remember, a positive correlation means that as one variable ( $x$ ) increases, the other variable ( $y$ ) tends to increase too.
They move in the same direction!

STEP 8

So, if on average, $y$ increases as $x$ increases, then yes, the correlation coefficient is positive.
It's true!

STEP 9

Even if we have a correlation coefficient ( $r$ ) close to 1 (a strong positive correlation) or close to -1 (a strong negative correlation), it doesn't prove that one variable causes the other to change.

STEP 10

A strong correlation just means they move together, not that one makes the other move.
There could be a third hidden variable influencing both of them!
That's why the answer is "An unidentified third variable could be influencing both variables under investigation."

STEP 11

1. I only
2. True
3. An unidentified third variable could be influencing both variables under investigation.

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Studdy Solution

STEP 1

STEP 2

1. Flood Insurance and Elevation2. Positive Correlation3. Correlation vs.Causation

STEP 3

Alright, let's break down these flood insurance scenarios!The first one says the cost goes *up* by $500\$500$500 for every foot higher the elevation.That means a *positive* relationship between elevation and cost.

STEP 4

The second scenario says the cost is always $10,000\$10,000$10,000, no matter the elevation.That means there's *no relationship* between elevation and cost.

STEP 5

The third scenario says the cost goes *down* by $500\$500$500 for every foot higher the elevation.That means a *negative* relationship between elevation and cost.

STEP 6

The problem implies a linear relationship between elevation and cost, and asks about the slope.Only scenario I describes a positive slope (cost increase per foot).

STEP 7

Remember, a positive correlation means that as one variable (xxx) increases, the other variable (yyy) *tends* to increase too.They move in the same direction!

STEP 8

So, if on average, yyy increases as xxx increases, then yes, the correlation coefficient is positive.It's *true*!

STEP 9

Even if we have a correlation coefficient (rrr) close to **1** (a strong positive correlation) or close to **-1** (a strong negative correlation), it doesn't *prove* that one variable *causes* the other to change.

STEP 10

A strong correlation just means they move together, not that one *makes* the other move.There could be a third hidden variable influencing *both* of them!That's why the answer is "An unidentified third variable could be influencing both variables under investigation."

STEP 11

1. I only2. True3. An unidentified third variable could be influencing both variables under investigation.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. Flood Insurance and Elevation
2. Positive Correlation
3. Correlation vs.
Causation

Alright, let's break down these flood insurance scenarios!
The first one says the cost goes up by $\$500$ for every foot higher the elevation.
That means a positive relationship between elevation and cost.

The second scenario says the cost is always $\$10,000$ , no matter the elevation.
That means there's no relationship between elevation and cost.

The third scenario says the cost goes down by $\$500$ for every foot higher the elevation.
That means a negative relationship between elevation and cost.

The problem implies a linear relationship between elevation and cost, and asks about the slope.
Only scenario I describes a positive slope (cost increase per foot).

Remember, a positive correlation means that as one variable ( $x$ ) increases, the other variable ( $y$ ) tends to increase too.
They move in the same direction!

So, if on average, $y$ increases as $x$ increases, then yes, the correlation coefficient is positive.
It's true!

Even if we have a correlation coefficient ( $r$ ) close to 1 (a strong positive correlation) or close to -1 (a strong negative correlation), it doesn't prove that one variable causes the other to change.

A strong correlation just means they move together, not that one makes the other move.
There could be a third hidden variable influencing both of them!
That's why the answer is "An unidentified third variable could be influencing both variables under investigation."

1. I only
2. True
3. An unidentified third variable could be influencing both variables under investigation.