Question

Total Snowfall and Number of Visitors at Yellowstone National Park
The tables below show the total snowfall (in inches) and the number of visitors to Yellowstone National
Park during 18 randomly selected weeks.

Total Snow Fall (inches)	8.3	28.9	13.8	10.7	23.5	24.8
Visitors	123,867	24,328	51,692	121,958	44,946	29,684
Total Snow Fall	28.3	29.7	5.3	1.3	21.3	16
Visitors	19,147	31,155	120,266	147,767	18,472	28,147
Total Snow Fall	0	29.7	0	2.5	6	24.4
Visitors	201,797	31,155	252,013	203,712	187,045	27,584

[1] Based on the variables involved in this relationship, which variable do you think is the explanatory
(x) variable and which do you think is the response (y) variable
Explanatory Variable: ___________________________________________
Response Variable: _____________________________________________
Use the statistics features of your calculator to calculate the correlation between the two variables.
r = ________
Interpret the full meaning of the correlation coefficient you calculated in #3, including the
direction, strength, and relationship between variables.

Use the statistics features of your calculator to calculate the average and SD for the variable you
chose as the explanatory variable.
Average = __________
SD = __________

Use the statistics features of your calculator to calculate the average and SD for the variable you
chose as the response variable.
Average = __________
SD = __________

Find the equation of the regression line that fits your data. SHOW ALL CALCULATIONS.

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

Interpret the meaning of the y-intercept of your regression model from question #7. If there is no
practical meaning, explain why.

Demonstrate how someone might use the regression model you found in question #7 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

(x) variable and which do you think is the response (y) variable
Explanatory Variable: :

Total Snow Fall (inches)

Response Variable:

Visitors

Use R studio to get the correlation coefficient

Rcode:

Total_Snow_Fall <- c(8.3,28.9,13.8,10.7,23.5,24.8,28.3,29.7,5.3,1.3,21.3,16,0,29.7,0,2.5,6,24.4)  
length(Total_Snow_Fall)
Visitors <- c(123867,24328,51692,121958,   44946,29684,19147,31155,120266,147767,18472,28147,201797,   31155,252013,   203712,   187045,   27584)
Visitors   
df=data.frame(Total_Snow_Fall,Visitors)
df
cor(df$Total_Snow_Fall,df$Visitors

Output:

-0.906446

ANSWER:

correlation coefficient =r=-0.906446

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

There exists a strong negative relationship between totalsnowfall and visitors.

as Total snow fall is more,visitors are less

and as Total snow fall is less ,visitors are more

Form:linear

Strength:Strong

Direction:Negative

Use the statistics features of your calculator to calculate the average and SD for the variable you
chose as the explanatory variable.
Rcode;

mean(df$Total_Snow_Fall)
sd(df$Total_Snow_Fall
Average = 15.25
SD = 11.19965

Use the statistics features of your calculator to calculate the average and SD for the variable you
chose as the response variable.

mean(df$Visitors)
sd(df$Visitors)
Average = 92485.28
SD =78078.66

slope=b=r*Sy/Sx=-(0.906446*78078.66)/11.19965=- 6319.313

y intercebt =a=ybar-b*xbar=92485.28-(- 6319.313)*15.25= 188854.8

Regression eq is

visitors=188854.8-6319.313*Total_Snow_Fall