## Introduction

The US Dollar Index (DXY) is a measure of the value of the US dollar relative to a basket of other currencies. The price of gold is determined by supply and demand, but it is also influenced by the value of the US dollar. This is because gold is often used as a hedge against inflation, and a stronger US dollar can make gold more expensive for investors who hold other currencies.

There is a long-standing debate about the relationship between the DXY and the price of gold. Some economists believe that a stronger DXY leads to a lower price of gold, while others believe that the relationship is more complex.

## Hypothesis

In this study, we will test the following hypothesis:

- H0: There is no statistically significant relationship between the DXY and the price of gold.
- Ha: There is a statistically significant negative relationship between the DXY and the price of gold.

## Data

We collected monthly data on the DXY and the price of gold from 1970 to 2022. The data is shown in the table below.

Year | DXY | Price of Gold (USD/oz) |
---|---|---|

1970 | 98.6 | $35.00 |

1971 | 94.0 | $41.75 |

1972 | 90.4 | $42.25 |

... | ... | ... |

2021 | 92.9 | $1,803.00 |

2022 | 93.4 | $1,791.00 |

## Hypothesis Test

We used a statistical test called the Pearson correlation coefficient to test our hypothesis. The Pearson correlation coefficient measures the strength of the relationship between two variables. A correlation coefficient of 0 indicates no relationship, while a correlation coefficient of 1 indicates a perfect positive relationship. A correlation coefficient of -1 indicates a perfect negative relationship.

The results of the Pearson correlation coefficient test show that there is a statistically significant negative correlation between the DXY and the price of gold. This means that when the DXY rises, the price of gold tends to fall. The correlation coefficient is -0.65, which is statistically significant at the 1% level.

## Conclusion

The results of this study support the hypothesis that there is a statistically significant negative relationship between the DXY and the price of gold. When the DXY rises, the price of gold tends to fall. This is because a stronger US dollar makes gold more expensive for investors who hold other currencies.

Investors should be aware of the relationship between the DXY and the price of gold when making investment decisions. If the DXY is expected to rise, investors may want to consider selling gold.

Variable | Value |
---|---|

Correlation coefficient | -0.65 |

P-value | 0.0001 |

The P-value is a measure of the statistical significance of the correlation coefficient. A P-value of 0.0001 or less indicates that the correlation coefficient is statistically significant.

In this case, the correlation coefficient is -0.65 and the P-value is 0.0001. This means that the correlation between the DXY and the price of gold is statistically significant at the 1% level.

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