Question

Use the data on snowfall and mood to create a regression equation. Then, you will use this regression equation to make predictions about negative affect levels. Using your graphing calculator, create a regression equation with the following data:

Monthly Snowfall and Mood

Total Daily Snowfall	Negative Affect Score
5in	10
3in	4
10in	24
12in	30
8in	12
10in	39
24in	50
36in	50
20in	47

Then, use this equation to predict Negative Affect Score for three different snowfall amounts not listed. Provide a 1-2 paragraph summary in which you address the following:

Present the regression equation.

Identify the three snowfall amounts you selected to predict Negative Affect Score for.

Identify the Negative Affect Score predicted for each.

Explain whether or not you agree with these predictions, and reflect on how appropriate regression is for these variables.

Answer 1

To first describe the data, we shall create a scatterplot to observe the apparent relationship of Y on X, where,
Y denotes the Negative Affect Scores
X denotes the Total Daily Snowfall
___________________________________________________________________________

#Using the following R code, we obtain the scatterplot :-

x=c(5,3,10,12,8,10,24,36,20)
y=c(10,4,24,30,12,39,50,50,47)

plot(x,y,main="Scatterplot of Mood on Snowfall",xlab="Total Daily Snowfall",ylab="Negative Afeect Score")
___________________________________________________________________________

The scatterplot is obtained as,

Interpretation :- It is very evident from the above plot, that there exist a logarithmic relationship between, Y and X.

So, I have decided to test the following no intercept regression model,

where,

___________________________________________________________________________

#Using the following R code, we obtain the fitted regression equation and its summary output,

fit=lm(y~-1+I(log(x)))
summary(fit)
___________________________________________________________________________

The fitted regression equation is obtained as,

As we can see from the above analysis, the adjusted r-squared value is 0.922 which depicts that 92.2% of the variability in Y is explained by log(X) in the above model, signifying that the model is a good fit.

3 snowfall amounts chosen to predict the Negative Affect score are taken as follows,

The predicted negative affect scores for the corresponding 3 Snowfall amount as stated above are obtained as follows,

Yes, I agree with the above predictions, because, as a result of the previous analysis, it is evident that the model is a very good fit with highly significant coefficients.
To visualize the position of the predicted observations, we shall create a scatterplot with the above results.