MHB Statistsics Mathematics Problem: Linear Regression

AI Thread Summary
The discussion focuses on finding the regression equation for predicting sodium content based on caloric content in hot dogs. Participants present the data in a table format and reference statistical formulas for calculating the regression coefficients. The key equations involve determining the slope (b1) and intercept (b0) using sums of squares and means. There is a request for assistance in calculating necessary values like n (the number of observations) and the mean of x (calories). The conversation emphasizes the correlation between caloric and sodium content, highlighting the relevance of linear regression in this context.
iamblessed20062
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Find the equation of the regression line for the given data. then construct A SCATTER PLOT of the data and draw the regression line. (each pair of variables has a significant correlation.) then use the regression equation to predict the value of y for each of the given x- values, if meaningful. the caloric content and the sodium content(in milligrams) for 6 beef ho dogs are shown in the table below. find the regression equation. y=_________________________ x +______________________________. (round to three decimal places as needed.) (a) x = 160 calories (b) x = 100 calories (c) x = 140 calories (d) x = 60 calories calories, x, 150, 170, 130, 120, 90, 180 sodium, y, 415, 465, 340, 370, 270, 550
 
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Hello and welcome to MHB, iamblessed20062! :D

It appears that given the calories of a hot dog, the sodium content can be predicted from this. I am going to present the data in tabular format, so that it is more easily read:

[table="width: 250, class: grid, align: left"]
[tr]
[td]Calories[/td]
[td]Sodium Content (mg)[/td]
[/tr]
[tr]
[td]150[/td]
[td]415[/td]
[/tr]
[tr]
[td]170[/td]
[td]465[/td]
[/tr]
[tr]
[td]130[/td]
[td]340[/td]
[/tr]
[tr]
[td]120[/td]
[td]370[/td]
[/tr]
[tr]
[td]90[/td]
[td]270[/td]
[/tr]
[tr]
[td]180[/td]
[td]550[/td]
[/tr]
[/table]

Now, according to my old Stats textbook, we have:

[box=green]Regression equation: $$\hat{y}=b_0+b_1x$$, where:

$$b_1=\frac{S_{xy}}{S_{xx}}$$

$$b_0=\frac{1}{n}\left(\sum y-b_1\sum x\right)$$

$$S_{xx}=\sum\left(x-\overline{x}\right)^2$$

$$S_{xy}=\sum\left(\left(x-\overline{x}\right)\left(y-\overline{y}\right)\right)$$[/box]

Can you proceed?
 
No, I cannot proceed from here.:-(
MarkFL said:
Hello and welcome to MHB, iamblessed20062! :D

It appears that given the calories of a hot dog, the sodium content can be predicted from this. I am going to present the data in tabular format, so that it is more easily read:

[table="width: 250, class: grid, align: left"]
[tr]
[td]Calories[/td]
[td]Sodium Content (mg)[/td]
[/tr]
[tr]
[td]150[/td]
[td]415[/td]
[/tr]
[tr]
[td]170[/td]
[td]465[/td]
[/tr]
[tr]
[td]130[/td]
[td]340[/td]
[/tr]
[tr]
[td]120[/td]
[td]370[/td]
[/tr]
[tr]
[td]90[/td]
[td]270[/td]
[/tr]
[tr]
[td]180[/td]
[td]550[/td]
[/tr]
[/table]

Now, according to my old Stats textbook, we have:

[box=green]Regression equation: $$\hat{y}=b_0+b_1x$$, where:

$$b_1=\frac{S_{xy}}{S_{xx}}$$

$$b_0=\frac{1}{n}\left(\sum y-b_1\sum x\right)$$

$$S_{xx}=\sum\left(x-\overline{x}\right)^2$$

$$S_{xy}=\sum\left(\left(x-\overline{x}\right)\left(y-\overline{y}\right)\right)$$[/box]

Can you proceed?
 
It seems like we should first compute $S_{xx}$. So, we need to identify $n$ and $\overline{x}$...can you find these?
 

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