Concept explainers
To find: The equation of the regression line and estimating the daily ticket sale on day 15th.
Answer to Problem 44SGR
The equation of regression line is
Explanation of Solution
Given: Daily ticket sale on different days since movie opened.
Concept Used: The general equation for a regression line is given as:
Where, Y is dependent and X is an independent variable. Also, a is the y-intercept and b is the slope of the line.
The values of a and b can be obtained by the following formulae:
Here, n is the number of observations used to estimate the regression line.
Calculation:
The table showing all the values corresponding to each observation is shown below:
Observation | Day of Sale ( | Daily Purchases ( | |||
1 | 1 | 185 | 185 | 1 | 34225 |
2 | 2 | 192 | 384 | 4 | 36864 |
3 | 3 | 189 | 567 | 9 | 35721 |
4 | 4 | 178 | 712 | 16 | 31684 |
5 | 5 | 165 | 825 | 25 | 27225 |
6 | 6 | 168 | 1008 | 36 | 28224 |
7 | 7 | 155 | 1085 | 49 | 24025 |
28 | 1232 | 4766 | 140 | 217968 |
From above table,
Hence, the equation of the regression line is obtained as:
Now, Let us estimate the ticket sale on day 15 since the movie has opened. For this,
Hence,
Conclusion: Thus, the equation of regression line is
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Algebra 1, Homework Practice Workbook (MERRILL ALGEBRA 1)
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