A box office analyst seeks to predict opening weekend box office gross for movies. Toward this goal, the analyst plans to use online trailer views as a predictor. For each of the 66 movies, the number of online trailer views from the release of the trailer through the Saturday before a movie opens and the opening weekend box office gross (in millions of dollars) are collected and stored in the accompanying table.Assuming a linear relationship, use the least-squares method to determine the regression coefficients b0 and b1.Interpret the meaning of the slope, b1, in this problem.Predict the mean opening weekend box office gross for a movie that had 80 million online trailer views.What insights can be obtained about predicting opening weekend box office gross from online trailer views? Online TrailerViews (millions)55.4948.9039.6866.86282.35737.67822.2857.9734.90046.0066.19427.6332.97659.3837.27713.39012.0652.3760.4535.9258.6344.92928.2090.2905.23611.11353.5625.68528.6395.37111.70360.95077.717Opening WeekendBox Office Gross($millions)34.1434.5743.64925.009104.42063.53919.0548.4117.33335.02422.79414.1486.114149.80810.3029.5221.6913.4270.4263.6713.3290.05897.7067.25811.32216.58248.4037.26216.8105.64713.86936.648176.486Online TrailerViews (millions)6.30637.2752.04143.3664.9896.6300.9422.25811.3278.96615.17713.71431.23152.61216.2356.88411.6982.82723.07512.6060.82627.5367.2733.3234.2673.7907.59712.9127.0675.0207.73916.7957.643Opening WeekendBox Office Gross(Smillions)5.08259.70317.47085.6784.69033.3773.7051.51318.47012.2024.35730.43653.00346.60713.0033.77618.2233.47113.60240.0111.38520.1303.4041.20710.9518.34411.61413.5015.1061.98522.80013.6892.080

The independent variable is Online Trailer Views. The dependent variable is Opening Weekend Box Office Gross. We have to find the coefficient of determination and interpretation. This is simple linear regression model.EXCEL (Data Analysis) Procedure: Step 1: In EXCEL sheet, enter Online Trailer Views in one column and enter Opening Weekend Box Office Gross in one column. Step 2: In Data, select Data Analysis and choose Regression. Step 3: In Input Variable Y Range: select Opening Weekend Box Office Gross. Step 4: In Input Variable X Range: select Online Trailer Views. Step 5: Select Lables. Click Ok. EXCEL (Data Analysis) output:The least squares regression equation is y^=-0.87 + 1.408 x. b0=-0.87 b1 = 1.408 Interpretation of b1: For each increase of $ 1 million online trailer views, the predicted opening weekend box office gross is expected to increase by $ 1.408 million. The nearest actual value of opening weekend box office gross for 80 million views is $ 176.486 million. The predicted mean opening weekend box office will be $ 0.98 million. As the number of online trailer views increases, the mean opening weekend box office gross can be expected to increase.

Answered: A box office analyst seeks to predict…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A box office analyst seeks to predict opening weekend box office gross for movies. Toward this goal, the analyst plans to use online trailer views as a predictor. For each of the 66 movies, the number of online trailer views from the release of the trailer through the Saturday before a movie opens and the opening weekend box office gross (in millions of dollars) are collected and stored in the accompanying table.

Assuming a linear relationship, use the least-squares method to determine the regression coefficients b0 and b1.

Interpret the meaning of the slope, b1, in this problem.

Predict the mean opening weekend box office gross for a movie that had 80 million online trailer views.

What insights can be obtained about predicting opening weekend box office gross from online trailer views?

Online Trailer
Views (millions)
55.494
8.903
9.686
6.862
82.357
37.678
22.285
7.973
4.900
46.006
6.194
27.633
2.976
59.383
7.277
13.390
12.065
2.376
0.453
5.925
8.634
4.929
28.209
0.290
5.236
11.113
53.562
5.685
28.639
5.371
11.703
60.950
77.717
Opening Weekend
Box Office Gross
($millions)
34.143
4.574
3.649
25.009
104.420
63.539
19.054
8.411
7.333
35.024
22.794
14.148
6.114
149.808
10.302
9.522
1.691
3.427
0.426
3.671
3.329
0.058
97.706
7.258
11.322
16.582
48.403
7.262
16.810
5.647
13.869
36.648
176.486
Online Trailer
Views (millions)
6.306
37.275
2.041
43.366
4.989
6.630
0.942
2.258
11.327
8.966
15.177
13.714
31.231
52.612
16.235
6.884
11.698
2.827
23.075
12.606
0.826
27.536
7.273
3.323
4.267
3.790
7.597
12.912
7.067
5.020
7.739
16.795
7.643
Opening Weekend
Box Office Gross
(Smillions)
5.082
59.703
17.470
85.678
4.690
33.377
3.705
1.513
18.470
12.202
4.357
30.436
53.003
46.607
13.003
3.776
18.223
3.471
13.602
40.011
1.385
20.130
3.404
1.207
10.951
8.344
11.614
13.501
5.106
1.985
22.800
13.689
2.080

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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