Posted on Categories:Regression Analysis, 回归分析, 统计代写, 统计代考

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## 统计代写|回归分析代写Regression Analysis代考|Graphical Representation of Regression Coefficients

A simple way to grasp regression coefficients and how they relate to the data is to display them on a fitted line plot. Towards this end, we’ll revisit the height-weight dataset. The fitted line plot illustrates this by graphing data points along with the relationship between a person’s height (IV) and weight (DV). The numeric output and the graph display information from the same model. Here is the CSV dataset: HeightWeight.
Coefficients
$\begin{array}{lrrrrr}\text { Term } & \text { Coef } & \text { SE Coef } & \text { T } & \text { P } \ \text { Constant } & -114.326 & 17.4425 & -6.55444 & 0.000 \ \text { Height M } & 106.505 & 11.5500 & 9.22117 & 0.000\end{array}$

The height coefficient in the regression equation is 106.5. This coefficient represents the mean increase of weight in kilograms for every additional one meter in height. This study sampled preteen girls in the United States. Consequently, if a preteen girl’s height increases by 1 meter, the average weight increases by $106.5$ kilograms.

The regression line on the graph visually displays the same information. If you move to the right along the $\mathrm{x}$-axis by one meter, the line increases by $106.5$ kilograms. Keep in mind that it is only safe to interpret regression results within the observation space of your data. And, we wouldn’t want to apply the model outside the target population of preteen girls. We don’t know the nature of the relationship between the variables outside the range of our dataset. It might change.

In this case, the height and weight data were collected from middleschool girls and range from approximately $1.3 \mathrm{~m}$ to $1.7 \mathrm{~m}$. Consequently, we can’t shift along the line by a full meter for these data.

## 统计代写|回归分析代写Regression Analysis代考|Example Regression Model with Two Linear Main Effects

Let’s interpret the results for the following multiple regression example:

Air Conditioning Costs $\$=2 *$Temperature$\mathrm{C}-1.5 *$Insulation CM In this model, we are using the temperature in Celsius and Insulation thickness in centimeters, our two independent variables, to explain air conditioning costs in dollars (dependent variable). The coefficient sign for Temperature is positive, which indicates a positive relationship between Temperature and Costs. As the temperature increases, so does air condition costs. More specifically, the coefficient value of 2 indicates that for every$1 \mathrm{C}$increase, the average value of the air conditioning costs increases by two dollars. On the other hand, the negative coefficient for insulation represents a negative relationship between insulation and air conditioning costs. As insulation thickness increases, air conditioning costs decrease. For every$1 \mathrm{CM}$increase, air condition costs drop by$\$1.50$.

Additionally, these are both main effects, which indicates that if you change the value of, say, insulation, the relationship between temperature and air condition costs remains the same. And, these are linear effects. For every $1 \mathrm{C}$ increase in temperature, air condition costs will always increase by $\$ 2$. It doesn’t matter if temperature increases from 20 to$21 \mathrm{C}$or from 30 to$31 \mathrm{C}$. That extra degree costs you$\$2$ !

However, you can’t extend that interpretation outside the range of your data. If you only measured up to $30 \mathrm{C}$, you can’t assume that the same relationship holds true at $35 \mathrm{C}$.

## MATLAB代写

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