Serial correlation, also known as autocorrelation, describes the extent to which the result in one period of a time series is related to the result in the next period. A time series with high serial correlation is said to be very predictable from one period to the next. If the serial correlation is low (or near zero), the time series is considered to be much less predictable. For more information about serial correlation, see the book Ibbotson SBBI published by Morningstar. An Internet advertising agency is studying the number of "hits" on a certain web site during an advertising campaign. It is hoped that as the campaign progresses, the number of hits on the web site will also increase in a predictable way from one day to the next. For 10 days of the campaign, the number of hits x 105 is shown. Original Time Series Day Hits x 105 2 4 9. 10 1.3 3.5 4.4 7.2 6.8 8.3 9.0 11.3 13.1 14.7 (a) To construct a serial correlation, we use data pairs (x, y) where x = (x, y) for serial correlation by filling in the following table. original data and y = original data shifted ahead by one time period. Construct the data set %D х 1.3 3.5 4.4 7.2 6.8 8.3 9.0 11.3 13.1

A movie studio wishes to determine the relationship between the revenue from rental of comedies on streaming services and the revenue generated from the theatrical release of such movies. The studio has the following bivariate data from a sample of fifteen comedies released over the past five years. These data give the revenue x from theatrical release (in millions of dollars) and the revenue y from streaming service rentals (in millions of dollars) for each of the fifteen movies. Also shown are the scatter plot and the least-squares regression line for the data. The equation for this line is y = 3.58 +0.15x. Theater revenue, x (in millions of dollars) 26.4 36.7 43.5 31.6 60.4 14.8 21.3 49.3 7.7 24.8 27.8 12.9 60.6 26.4 66.4 Send data to calculator V Rental revenue, y (in millions of dollars) 8.1 12.4 6.8 5.1 15.4 2.6 5.8 16.5 2.2 9.1 3.3 9.8 10.8 11.7 9.6 Based on the studio's data and the regression line, complete the following. Rental revenue in millions of dollars) 0 X 10 X 20…

An ecologist is interested in exploring the relationship between pollination rate and the number of bees present at apple orchards. The relationship is: (Pollination rate) = 372.6 + 13.5 x (bees) with r = 0.80. The best interpretation of the correlation coefficient is: (pick one) 1. 64% of the variability in pollination rate observed at apple orchards is explained by the relationship with the number of bees 2. the correlation between pollination rate and number of bees is 0.64 3. 80% of the variability in number of bees at apple orchards is explained by the relationship with the pollination rate 4. the correlation between pollination rate and number of bees is 0.80

In a regression study, relating Price/unit (x) to Weekly Sales (in Kg.), with the scatter plot showing a strong negative direction, 63% of the variability in sales could be accounted for by the variation in the Unit Price. The correlation coefficient in this study is: 0.79 -0.4 -0.79 0.4

What information is provided by r2? What are the primary uses of partial correlations?

A nutritionist collects data from 25 popular breakfast cereals. For each cereal, the number of calories per serving is plotted on the x-axis against the number of milligrams of sodium on the y-axis. The value of r for the resulting scatterplot is 0.83. How would the value of the correlation coefficient, r, change if sodium was plotted on the x-axis and calories plotted on the y-axis? The value of r would increase. The value of r would not change. The value of r would change to –0.83. The value of r could increase or decrease, depending of the strength of the new relationship.

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