Data606 Presentation
Dhananjay Kumar
7.23 Tourism spending. The Association of Turkish Travel Agencies reports the number of foreign tourists visiting Turkey and tourist spending by year.20 Three plots are provided: scatter- plot showing the relationship between these two variables along with the least squares t, residuals plot, and histogram of residuals.
Fig. 7.23.
(a) Describe the relationship between number of tourists and spending.
(b) What are the explanatory and response variables?
(c) Why might we want to fit a regression line to these data?
(d) Do the data meet the conditions required for fitting a least squares line? In addition to the scatterplot, use the residual plot and histogram to answer this question.
Answer :
(a) The relatonship is linear and has a strong positive correlation.
(b) The explanatory varibale is Number of Tourists and response is Spending
(c) The relationship looks linear as seen from the scatter plot, therefore we might want to fit a regression line to this data.
(d) The conditions for least squared line are:
Linear trend: The first plot shows the linear trend, so this condition is met.
Residuals should be nearly normal: The histogram of the residuals is nearly normal so this condition is met.
Constant variability: From the second graph the variance is not constant, so this condition is not met.
Observation independent: Since these observation are not from time series, we assume they are independent.
Since the varinace is not constant, the data does not meet the required condition for fitting the least squared line (regression line)
2.5 Coin flips If you flip a fair coin 10 times, what is the probability of
- getting all tails?
Answer Assume each flip is independent, then (1/2)^10 = 1/1024.
- getting all heads?
Answer Assume each flip is independent, then (1/2)^10 = 1/1024.
- getting at least one tails?
Answer The probability of getting at least 1 tail is 1 - (1 / 1024) = 1023 / 1024.