Month: December 2018

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Correlation – Statistic

Correlation in a statistic is a factor used to describe the relationship between one variable and the other variable. In a graph, there are two axes: X-axis (explanatory variable) and Y-axis (responses variable). For example, If we would use height to predict weight then the height would be the explanatory variable and the weight would be the response variable. Then we would use the data of the height and the weight to calculate for the correlation coefficient (r).

 

The correlation coefficient(r), rage from -1 to 1. When the r-value equal to -1, it shows that the two variables have a negative relationship/correlation; in this case, it means that as the height increase, the predicted weight will decrease. On the other hand, if the r-value would to equal to 1, the two variables will have a positive relationship/correlation which means that as the height increase the weight will also increase. Yet, if the r-value equal to 0, the two variables don’t have any relationship at all. However, a perfect r-value of -1, 0, or 1 is not a value that we’ll get calculating real datasets because real datasets won’t have such an exact relationship between real datasets.

 

The equation for r is r =1/n-1∑(xi-x/xs)(yi-y/ys), however, it would take forever to plug in and solve this equation; so we use the Ti3 calculator instead. In our case of using height to predict weight, we receive an r-value of .76. This value shows a high correlation between the two variables, therefore, it’s positive to use the height to predict the weight.

Watch me solving for the r and r-square value!

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Lewis Dot Structure and VSEPR Model

This round in chemistry essential, I have learned so many new concepts that manoeuvre me deeper into the world of chemistry. For instance, we were learning about the Lewis Dot Structure and Vsepr Model. These two concepts were very interesting to me because it gives me a better sense of how chemical bond together at the atom level.

Lewis dot structure is a diagram that shows how atoms are bonding together and how many lone pairs of electrons are there in the molecule. For example, if we have an element of Phosphorus trifluoride (PF3), we would start off by looking for the valence electrons. In this case, the valence electrons for Phosphorus and the three Fluorine is 5 and 21 respectively. Then, we would draw P (symbol for Phosphorus) in the middle of the diagram since it’s less electronegative with five dots (representing the valence electrons) around it. However, the dots can’t just be laying everywhere around the P: It needs to be placed on the four sides of the P (top, right, bottom, and left.) Then we need to define the bonding between P and the three Fluorine (F3). Since Phosphorus has three valence electrons, it only needs 3 more to get to the stable stage. Therefore, it can share its three individuals electrons with the other three individuals electrons from the three fluorine. So we can draw three lines from P to the three fluorine with a free pair of electrons on the top of P and 6 free pairs of electrons around each F.

Lewis dot structure of PF3

Afterwards, we can also turn this structure into a 3D model using the VSEPR model. Since this diagram got three bonds with a free pair of electrons on the centre atom, it falls under the category of Trigonal Pyramidal.

VSEPR model of PF3
3D VSEPR model of PF3