MAT 240 Module 7 Journal Aid

This content provides a detailed walkthrough of a journal assignment for MAT 240, focusing on regression analysis using weather data. The video aid explains how to use StatCrunch to analyze the correlation between July and August temperatures and precipitation. It demonstrates how to interpret p-values, scatter plots, and regression lines to determine if there is a significant relationship between the variables. The guide emphasizes the importance of understanding the results in the context of real-world questions and cautions that weather patterns can be very local, so results may vary.

MAT 240 Module 7 Journal Aid Transcript
This video is an aid for the journal assignment in week 7 of MAT240.
In weeks 6 and 7, we’ve been looking at regression analysis. They topic of this journal in week 7 is …
regression analysis. We will be looking at 2 different problems:
One of them relates low temps in July and August. We’re interested in knowing “do hot Augusts follow
hot Julys… do cool Augusts follow cool Julys”, in other words is there a correlation between the temps in
July and August. Before doing the analysis, I would say “I don’t know”.
Then, the second regression is to compare the precipitation or rainfall in July and August. The same
question “do rainy Augusts follow rainy Julys and dry Augusts follow dry Julys”? Here again I’m not sure.
I’m not a meteorologist.
[1:50] For our first regression, we’ve been looking at the variable MMNT, the mean minimum
temperature. For this analysis, I’ve chosen just the July and August temperatures. We want to know
whether they are correlated. In other words, do hot Augusts follow hot Julys. Or maybe, do cool Augusts
follow hot Julys. So we want to do a regression model. Since August is the later month in time, it makes
sense to have August as our Y variable and July as our X variable. We’re not too good at time travel, so
predicting forwards is the way to go.
We have a linear model
Min_Aug = slope times Min_July + intercept
[3:15] We want to test whether the slope is 0 or different from 0. Rejecting the null means a correlation.
Not rejecting the null means insufficient evidence to show a correlation.
So what do we do? We go to StatCrunch. You should be very familiar by now. I’ve already logged in … I
open StatCrunch and I get a blank dataset. We load from Shared Datasets and, as usual, searching for
snhu mat240 … and we see Central Park and the Journal. Of course, I’m going to do Central Park again –
you need to do your Journal.
[4:45] Here is the data. The new variables are all the way to the right. In 1876, it was 22.2 degrees
Celsius as the mean minimum in July and 20.1 Celsius as the mean minimum in August.
We can jump right into regression because the regression output will give us some information to assess
the quality of this model. Stat – Regression – Simple Linear. Simple means one X variable. We’re using
July’s minimum to predict August’s minimum. Compute … and there are two screens.
[6:10] The first screen is numeric. You can see that the p-value for the slope is less than .0001 – that
means an extremely strong correlation. The slope is positive – that means an extremely strong positive
correlation. So what the data show, at least for Central Park New York, is that July and August
temperatures are positively correlated. That means hot Augusts follow hot Julys in general, and cool
Augusts follow cool Julys, in general.

You see at the bottom here there is a > sign. It also says 1 of 2 on the top. That means that there is a
second page.
[7:20] And the second page is very useful. This is a scatter plot. We see that the x axis is the minimum for
July and the y axis is the minimum for August. We see all the dots, and StatCrunch has drawn in red the
regression line.
Maybe it’s not entirely clear that this is positive correlation, but our calculations are very sensitive and
this is an extremely strong positive correlation.
Before doing the second part, let me just, as usual, shrink this and move it to the side. It’s going to be
useful to compare to the next one.
[8:35] Here we see the other two variables, the precipitation in July and the precipitation in August.
We’d like to do a similar regression. We want to see if there is a correlation between rain in July and rain
in August. Stat – Regression – Simple Linear.
We want to use … can’t quite see … the precipitation in July to predict … I’m choosing … the
precipitation in August. Compute. And here are the results for our precipitation regression.
[9:40] Here’s a very major difference. The p-value is .7. Remember p-value measures how unlikely this is.
.7 is pretty high … this is NOT unlikely. So our conclusion would be to not reject the null hypothesis.
There is no significant evidence that the precipitation in August and the precipitation in July are
correlated. The rainfall seems to be pretty independent.
Again, let me click this > … to look at the scatter plot. You see here that the points don’t really show any
pattern going up or going down. You can see that the fitted line is very flat. So let me move this window
a little bit so that we can compare our two regressions. I want to move them so that we can see both
scatter plots at the same time.
[11:15] The bottom scatter plot was for temperature. You can see, by eye, that there is a trend going up.
Usually when you can see by eye, it means that there is a significant correlation.
For the precipitation, you cannot see any trend by eye. That doesn’t mean that there isn’t significant
correlation, but our calculation does show that there is no significant relationship between the two.
These are the results for Central Park. A word of warning: weather is very local, as you know. Just
because Central Park has these results does not mean that your Journal database will have these results.
Make sure that you interpret your results in terms of temperature and rainfall. After all, that’s the
purpose of statistical analysis – to answer real world questions.