Help Interpreting expression with lots of summations

[Hckyplayer8]

Hello! I would like help interpreting the above. I'm in a programming course for MATLAB and we are computing the slope of two different data sets. Set X are years laid out at 1 year increments from 1960 to 2000. Set Y is CO2 concentration for that respective year. So n=41 for both sets of data.

I'm familiar with the traditional delta Y divided by delta X for slope but I'm looking for a refresher and confirmation of the above.


Does this say to sum the individual x values from x sub 1 (in this case 1960) to the n value (in this case 2000)?


Does this mean the same as the above, just for the y values?


Is this saying to multiple the n-th value (41) by the previously two found values?

Thanks for your time!

 

[Harry_the_cat]

View attachment 35360
Hello! I would like help interpreting the above. I'm in a programming course for MATLAB and we are computing the slope of two different data sets. Set X are years laid out at 1 year increments from 1960 to 2000. Set Y is CO2 concentration for that respective year. So n=41 for both sets of data.

I'm familiar with the traditional delta Y divided by delta X for slope but I'm looking for a refresher and confirmation of the above.

View attachment 35361
Does this say to sum the individual x values from x sub 1 (in this case 1960) to the n value (in this case 2000)?

View attachment 35362
Does this mean the same as the above, just for the y values?

View attachment 35363
Is this saying to multiple the n-th value (41) by the previously two found values?

Thanks for your time!

=\(\displaystyle x_1 + x_2 + x_3 + ... + x_{41}\)

Same for y's.

= \(\displaystyle 41\times (x_1\times y_1 + x_2\times y_2 +x_3\times y_3 + ... + x_{41}\times y_{41})\),

that is, multiply the corresponding x and y's, add all together, multiply the total by 41.

 

[Hckyplayer8]

View attachment 35365 =\(\displaystyle x_1 + x_2 + x_3 + ... + x_{41}\)

Same for y's.

View attachment 35366 = \(\displaystyle 41\times (x_1\times y_1 + x_2\times y_2 +x_3\times y_3 + ... + x_{41}\times y_{41})\),

that is, multiply the corresponding x and y's, add all together, multiply the total by 41.

Thanks for the quick replay Harry_the_cat! I appreciate it!

 

[Steven G]

Is this saying to multiple the n-th value (41) by the previously two found values?

There is no n-th value. However, there is a value for n.