The table shows data on the number of visitors to the UK in a month, v (1000s), and the amount of money they spent, m (£ millions), for each of 8 months. Number of visitors 2450 2480 2540 2420 2350 2290 2400 2460 v (1000s) Amount of money spent 1370| 1350 1400 1330 1270 1210 1330 1350 m (£ millions) The correlation coefficient between m and v is 0.962 a. Give a reason to support fitting a regression model of the form m = a + bv to these data. b. Summary statistics are: v = 2423.75, m = 1326.25, s, = 77.9995421, sm = 1326.25, R = 0.962 For a regression model of the form m = a + bv . Find the value of b (the slope) correct to two decimal places. c. Now calculate a (the intercept) to calculate the regression model. d. Interpreting the value of b, each additional visitor spends £ e. Using the equation calculated in part c, estimate the amount of money spent when the number of visitors to the UK in a month is 2,500,000
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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