(a) To construct a serial correlation, we use data pairs (x, y) where x = original data and y = original data shifted ahead by one time period. Construct the data set (x, y) for serial correlation by filling in the following table. x 1.2 3.5 4.4 7.3 6.7 8.1 9.0 11.2 13.1 y (b) For the (x, y) data set of part (a), compute the equation of the sample least-squares line ŷ = a + bx. (Use 4 decimal places.) a b If the number of hits was 9.3 (× 105) one day, what do you predict for the number of hits the next day? (Use 1 decimal place.) (× 105) hits (c) Compute the sample correlation coefficient r and the coefficient of determination r2. (Use 4 decimal places.) r r2 Test ρ > 0 at the 1% level of significance. (Use 2 decimal places.) t critical t
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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
is shown.
| Day | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Hits × 105 | 1.2 | 3.5 | 4.4 | 7.3 | 6.7 | 8.1 | 9.0 | 11.2 | 13.1 | 14.8 |
| x | 1.2 | 3.5 | 4.4 | 7.3 | 6.7 | 8.1 | 9.0 | 11.2 | 13.1 |
| y |
(b) For the
| a | |
| b |
If the number of hits was
(c) Compute the sample
| r | |
| r2 |
Test
| t | |
| critical t |
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
