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Matthew Gunn
Matthew Gunn
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No, a non-zero $\beta_3$ does not imply $A$ and $B$ are correlated. It implies $y$ is correlated with $AB$.

TrivialSimple example:

Imagine we have data on visits by people to a gas station.

  • Let $A$ be the volume of someone's gas tank in gallons.
  • Let $B$ be the price of gas at the time of the visit.
  • Let $y$ be the spending on gas this visit.

$A \cdot B$ is how much it would cost to fill the person's gas tank. $AB$ is almost certainly correlated with $y$, the spending on gas this visit.

A positive $\beta_3$ in this trivial example does not imply that the size of someone's gas tank is correlated with the price of gas. A positive $\beta_3$ would mean that spending $y$ is positive related to the carrying capacity of someone's gas tank measured in dollars (i.e. $AB$).

No, a non-zero $\beta_3$ does not imply $A$ and $B$ are correlated. It implies $y$ is correlated with $AB$.

Trivial example:

Imagine we have data on visits by people to a gas station.

  • Let $A$ be the volume of someone's gas tank in gallons.
  • Let $B$ be the price of gas at the time of the visit.
  • Let $y$ be the spending on gas this visit.

$A \cdot B$ is how much it would cost to fill the person's gas tank. $AB$ is almost certainly correlated with $y$, the spending on gas this visit.

A positive $\beta_3$ in this trivial example does not imply that the size of someone's gas tank is correlated with the price of gas. A positive $\beta_3$ would mean that spending $y$ is positive related to the carrying capacity of someone's gas tank measured in dollars (i.e. $AB$).

No, a non-zero $\beta_3$ does not imply $A$ and $B$ are correlated. It implies $y$ is correlated with $AB$.

Simple example:

Imagine we have data on visits by people to a gas station.

  • Let $A$ be the volume of someone's gas tank in gallons.
  • Let $B$ be the price of gas at the time of the visit.
  • Let $y$ be the spending on gas this visit.

$A \cdot B$ is how much it would cost to fill the person's gas tank. $AB$ is almost certainly correlated with $y$, the spending on gas this visit.

A positive $\beta_3$ in this trivial example does not imply that the size of someone's gas tank is correlated with the price of gas. A positive $\beta_3$ would mean that spending $y$ is positive related to the carrying capacity of someone's gas tank measured in dollars (i.e. $AB$).

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Matthew Gunn
Matthew Gunn
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No, a non-zero $\beta_3$ does not imply $A$ and $B$ are correlated. It implies $y$ is correlated with $AB$.

Trivial example:

Imagine we have data on visits by people to a gas station.

  • Let $A$ be the volume of someone's gas tank in gallons.
  • Let $B$ be the price of gas at the time of the visit.
  • Let $y$ be the spending on gas this visit.

$A \cdot B$ is how much it would cost to fill the person's gas tank. $AB$ is almost certainly correlated with $y$, the spending on gas this visit.

A positive $\beta_3$ in this trivial example does not imply that the size of someone's gas tank is correlated with the price of gas. A positive $\beta_3$ would mean that spending $y$ is positive related to the carrying capacity of someone's gas tank measured in dollars (i.e. $AB$).

No, a non-zero $\beta_3$ does not imply $A$ and $B$ are correlated. It implies $y$ is correlated with $AB$.

Trivial example:

Imagine we have data on visits by people to a gas station.

  • Let $A$ be the volume of someone's gas tank in gallons.
  • Let $B$ be the price of gas at the time of the visit.
  • Let $y$ be the spending on gas this visit.

$A \cdot B$ is how much it would cost to fill the person's gas tank. $AB$ is almost certainly correlated with $y$, the spending on gas this visit.

A positive $\beta_3$ in this trivial example does not imply that the size of someone's gas tank is correlated with the price of gas.

No, a non-zero $\beta_3$ does not imply $A$ and $B$ are correlated. It implies $y$ is correlated with $AB$.

Trivial example:

Imagine we have data on visits by people to a gas station.

  • Let $A$ be the volume of someone's gas tank in gallons.
  • Let $B$ be the price of gas at the time of the visit.
  • Let $y$ be the spending on gas this visit.

$A \cdot B$ is how much it would cost to fill the person's gas tank. $AB$ is almost certainly correlated with $y$, the spending on gas this visit.

A positive $\beta_3$ in this trivial example does not imply that the size of someone's gas tank is correlated with the price of gas. A positive $\beta_3$ would mean that spending $y$ is positive related to the carrying capacity of someone's gas tank measured in dollars (i.e. $AB$).

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Matthew Gunn
Matthew Gunn
  • 23k
  • 1
  • 62
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No, a non-zero $\beta_3$ does not imply $A$ and $B$ are correlated. It implies $y$ is correlated with $AB$.

Trivial example:

Imagine we have data on visits by people to a gas station.

  • Let $A$ be the volume of someone's gas tank in gallons.
  • Let $B$ be the price of gas in dollars per gallon at the time of the visit.
  • Let $y$ be the spending on gas this visit (in dollars).

$A \cdot B$ is how much it would cost to fill the person's gas tank, and that's. $AB$ is almost certainly correlated with $y$, the number of dollars they spendspending on gas this gas station visit.

A positive $\beta_3$ in this trivial example does not imply that the size of someone's gas tank is correlated with the price of gas.

No, a non-zero $\beta_3$ does not imply $A$ and $B$ are correlated. It implies $y$ is correlated with $AB$.

Trivial example:

Imagine we have data on visits by people to a gas station.

  • Let $A$ be the volume of someone's gas tank in gallons.
  • Let $B$ be the price of gas in dollars per gallon at the time of the visit.
  • Let $y$ be the spending on gas this visit (in dollars).

$A \cdot B$ is how much it would cost to fill the person's gas tank, and that's almost certainly correlated with $y$, the number of dollars they spend on gas this gas station visit.

A positive $\beta_3$ in this trivial example does not imply that the size of someone's gas tank is correlated with the price of gas.

No, a non-zero $\beta_3$ does not imply $A$ and $B$ are correlated. It implies $y$ is correlated with $AB$.

Trivial example:

Imagine we have data on visits by people to a gas station.

  • Let $A$ be the volume of someone's gas tank in gallons.
  • Let $B$ be the price of gas at the time of the visit.
  • Let $y$ be the spending on gas this visit.

$A \cdot B$ is how much it would cost to fill the person's gas tank. $AB$ is almost certainly correlated with $y$, the spending on gas this visit.

A positive $\beta_3$ in this trivial example does not imply that the size of someone's gas tank is correlated with the price of gas.

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Matthew Gunn
Matthew Gunn
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Matthew Gunn
Matthew Gunn
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Matthew Gunn
Matthew Gunn
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Source Link
Matthew Gunn
Matthew Gunn
  • 23k
  • 1
  • 62
  • 95