Question

A company that holds the DVD distribution rights to movies previously released only in theaters has the business objective of developing estimates of the sales revenue of DVDs. Toward this goal, a company analyst plans to use box office gross to predict DVD sales revenue. For 43 movies, the analyst collects the box office gross (in $millions) in the year that they were released and the DVD revenue (in $millions) in the following year and stores these data here.

What are the values for

(1) the proportion of variation in DVD sales revenue that is explained by box office gross ,

(2) the sum of squares Y ,

(3) the sum of squares predicted ,

(4) the sum of squares error ,

(5) the intercept A ,

(6) the slope b ,

(7) the predicted sales revenue (in $millions) for a movie DVD that had a box office gross of $100 million

(8) the standard error of estimate ? Hint: Use PHStat to obtain all the values and answers should be accurate to 4 decimal places.

Title	Gross	DVD Revenue
Harry Potter & the Deathly Hollows: Part 1I	381.01	94.43
Transformers: Dark of the Moon	352.39	44.78
The Hangover Part II	254.46	35.39
Pirates of the Caribbean:On Stranger Tides	241.06	17.86
Fast Five	210.03	30.63
Cars 2	191.45	73.12
Thor	181.03	19.85
Rise of the Planet of the Apes	176.76	27.03
Capatin America: The First Avenger	176.65	21.49
Bridesmaids	169.21	52.75
The Help	169.50	54.59
Kung Fu Panda 2	165.25	24.94
X-Men First Class	146.41	23.19
Puss in Boots	145.74	44.98
The Smurfs	142.61	28.96
Mission Impossible:Ghost Protocol	141.19	22.58
Sherlock Holmes: A Game of Shadows	136.91	44.70
Super Eight	127.00	14.57
Rango	123.48	22.63
Horrible Bosses	117.54	16.76
Green Lantern	116.60	16.89
The Lion King	109.95	20.49
Cowboys and Aliens	100.37	17.39
Real Steel	84.49	24.91
Crazy Stupid Love	84.39	15.39
The Muppets	83.56	27.99
Battle:Los Angeles	83.55	13.28
Immortals	82.70	18.60
Zookeeper	80.36	11.93
Limitless	79.25	11.19
Tower Heist	76.80	14.10
Moneyball	75.02	19.23
Justin Bieber: Never Say Never	73.01	23.67
DolphinTale	72.02	13.63
Jack and Jill	71.75	11.67
Mr. Popper's Penguins	68.22	16.30
Happy Feet 2	60.97	19.54
Water for Elephants	58.71	13.21
The Lincoln Lawyer	58.01	10.65
Hugo	50.31	17.42
New Year's Eve	47.26	8.68
Arthur Christmas	46.07	12.28
War Horse	44.09	24.94

Answer 1

(1) the proportion of variation in DVD sales revenue that is explained by box office gross ,

0.5123

(2) the sum of squares Y ,

12,570.0250

(3) the sum of squares predicted ,

6,439.6133

(4) the sum of squares error ,

6,130.4117

(5) the intercept A ,

4.8445

(6) the slope b ,

0.1631

(7) the predicted sales revenue (in $millions) for a movie DVD that had a box office gross of $100 million

21.1588

(8) the standard error of estimate ? Hint: Use PHStat to obtain all the values and answers should be accurate to 4 decimal places.

12.2279

The regression output is:

	r²	0.5123
	r	0.716
	Std. Error	12.2279
	n	43
	k	1
	Dep. Var.	DVD Revenue
ANOVA table
Source	SS	df	MS	F	p-value
Regression	6,439.6133	1	6,439.6133	43.07	6.86E-08
Residual	6,130.4117	41	149.5222
Total	12,570.0250	42
Regression output					confidence interval
variables	coefficients	std. error	t (df=41)	p-value	95% lower	95% upper
Intercept	4.8445
Gross	0.1631	0.0249	6.563	6.86E-08	0.1129	0.2133
Predicted values for: DVD Revenue
		95% Confidence Interval		95% Prediction Interval
Gross	Predicted	lower	upper	lower	upper	Leverage
100	21.1588	17.15791	25.15977	-3.85797	46.17565	0.026