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
Messages
2
Reaction score
0
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
 
Mathematics news on Phys.org
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?
 
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Back
Top