Question

Total Snowfall (inches)	11	18	18	13	22	22	21	30	24
Visitors	13	14	18	15	22	22	29	44	29
Total Snowfall (inches)	45	27	59	33	49	51	31	64	23
Visitors	36	37	42	43	47	51	49	61	51
Total Snowfall (inches)
Visitors

Total Snowfall and Number of Visitors at Yellowstone National Park

The table above shows the total snowfall (in inches) and the number of visitors to Yellowstone National Park during 18 randomly selected weeks. (Show all calculations)

1. Based on the variables involved in this relationship which variable do you think is the explanatory (x) variable and which is the response (y) variable?

2. Calculate the correlation between the two variables. r=

3. Interpret the full meaning of the correlation coefficient you calculated in #2, including direction, strength, and relationship between variables.

4. Calculate the average and SD for the variable you chose as the explanatory variable.

Average =

SD =

5. Calculate the average and SD for the variable you chose as the response variable.

Average=

SD=

6. Find the equation of the regression line that fits your data. Show all calculation.

7. Interpret the meaning of the slope of your regression model from question #6

8. Interpret the meaning of the y-intercept of your regression model from question #6. If there is no practical meaning, explain why.

9. Demonstrate how someone might use the regression model you found in question #6 to predict the value of a response variable. That is, plug a hypothetical x-value in your model and explain what it predicts.

Answer 1

1. Based on the variables involved in this relationship total snowfall is the explanatory (x) variable and Number of visitors is the response variable.

I used Excel for calculation purpose.

Total snow fall (X)	Number of visitors (Y)
11	13
18	14
18	18
13	15
22	22
22	22
21	29
30	44
24	29
45	36
27	37
59	42
33	43
49	47
51	51
31	49
64	61
23	51
Correlation =	CORREL(A2:A19,B2:B19)	0.77819576
Mean (X)	AVERAGE(A2:A19)	31.166667
Mean(Y)	AVERAGE(B2:B19)	34.611111
SD(X)	STDEV(A2:A19)	15.81231836
SD(Y)	STDEV(B2:B19)	14.84880224

Que.2

The correlation between two variables = r = 0.7782

Que.3

Since correlation coefficient is positive and greater than 0.5, we conclude that there is high degree positive correlation between snowfall and number of visitors. It means if snowfall increases then number of visitors also increases.

Que.4

Average and standard deviation for the explanatory variable (total snowfall) are as follows:

Average = 31.1667

SD = 15.8123

Que.5

Average and standard deviation for the response variable (visitors) are as follows:

Average = 34.6111

SD = 14.8488