### 统计代写|回归分析作业代写Regression Analysis代考|STA321

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|回归分析作业代写Regression Analysis代考|Interpret the Pearson’s Correlation Coefficient

What do the correlation and p-value mean? We’ll interpret the output soon. First, let’s look at a range of possible correlation values so we can understand how our height and weight example fits in.

Pearson’s correlation coefficient is represented by the Greek letter rho ( $\rho$ ) for the population parameter and $r$ for a sample statistic. This coefficient is a single number that measures both the strength and direction of the linear relationship between two continuous variables. Values can range from $-1$ to $+1$.

• Strength: The greater the absolute value of the coefficient, the stronger the relationship.
• The extreme values of $-1$ and 1 indicate a perfectly linear relationship where a change in one variable is accompanied by a perfectly consistent change in the other. For these relationships, all of the data points fall on a line. In practice, you won’t see either type of perfect relationship. A coefficient of zero represents no linear relationship. As one variable increases, there is no tendency in the other variable to either increase or decrease.
• When the value is in-between 0 and $+1 /-1$, there is a relationship, but the points don’t all fall on a line. As $r$

approaches $-1$ or 1 , the strength of the relationship increases and the data points tend to fall closer to a line.

• Direction: The coefficient sign represents the direction of the relationship.
• Positive coefficients indicate that when the value of one variable increases, the value of the other variable also tends to increase. Positive relationships produce an upward slope on a scatterplot.
• Negative coefficients represent cases when the value of one variable increases, the value of the other variable tends to decrease. Negative relationships produce a downward slope.
Examples of Positive and Negative Correlations
An example of a positive correlation is the relationship between the speed of a wind turbine and the amount of energy it produces. As the turbine speed increases, electricity production also increases.

An example of a negative correlation is the relationship between outdoor temperature and heating costs. As the temperature increases, heating costs decrease.

## 统计代写|回归分析作业代写Regression Analysis代考|Discussion about the Correlation Scatterplots

For the scatterplots above, I created one positive relationship between the variables and one negative relationship between the variables. Then, I varied only the amount of dispersion between the data points and the line that defines the relationship. That process illustrates how correlation measures the strength of the relationship. The stronger the relationship, the closer the data points fall to the line. I didn’t include plots for weaker correlations that are closer to zero than $0.6$ and $-0.6$ because they start to look like blobs of dots and it’s hard to see the relationship.

A common misinterpretation is that a negative correlation coefficient indicates there is no relationship between a pair of variables. After all, a negative correlation sounds suspiciously like no relationship. However, the scatterplots for the negative correlations display real relationships. For negative relationships, high values of one variable are associated with low values of another variable. For example, there is a negative correlation between school absences and grades. As the number of absences increases, the grades decrease.

Earlier I mentioned how crucial it is to graph your data to understand them better. However, a quantitative assessment of the relationship does have an advantage. Graphs are a great way to visualize the data, but the scaling can exaggerate or weaken the appearance of a relationship. Additionally, the automatic scaling in most statistical software tends to make all data look similar.

Fortunately, Pearson’s correlation coefficient is unaffected by scaling issues. Consequently, a statistical assessment is better for determining the precise strength of the relationship.

Graphs and the relevant statistical measures often work better in tandem.

## 统计代写|回归分析作业代写Regression Analysis代考|Interpret the Pearson’s Correlation Coefficient

• 强度：系数的绝对值越大，关系越强。
• 的极值−1和 1 表示完全线性关系，其中一个变量的变化伴随着另一个变量的完全一致的变化。对于这些关系，所有数据点都落在一条线上。实际上，您不会看到任何一种完美关系。系数为零表示没有线性关系。当一个变量增加时，另一个变量没有增加或减少的趋势。
• 当值介于 0 和+1/−1，有关系，但点并不都落在一条线上。作为r

• 方向：系数符号代表关系的方向。
• 正系数表示当一个变量的值增加时，另一个变量的值也有增加的趋势。正相关在散点图上产生向上的斜率。
• 负系数表示当一个变量的值增加时，另一个变量的值趋于减小的情况。负面关系产生向下的斜率。
正相关和负相关
的示例 正相关的示例是风力涡轮机的速度与其产生的能量之间的关系。随着涡轮速度的增加，发电量也增加。

## 广义线性模型代考

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## MATLAB代写

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