A company that holds the DVD distribution rights to movies previously released only in theatres has the business objecti
Posted: Wed May 04, 2022 12:12 pm
A company that holds the DVD distribution rights to movies
previously released only in theatres has the business objective of
developing estimates of the sales revenue of DVDs. Towards this
goal, a company analyst plans to use box office gross to predict
DVD sales revenue. For 22 movies, the analyst collects the box
office gross (in $millions) in the year that they were released and
DVD revenue (in $millions) in the following year. The data are
stored in DVD Revenue.xlsx
For these data, assuming all the conditions and assumptions for
inference are satisfied:
a) Construct a scatterplot.
i) Write down the explanatory variable and response
variable
NOTE: Copy and paste the following wordings (highlighted
in yellow) into the section below as is
appropriate. Use only the highlighted wordings. Do not
add any extra space or symbol when copying and pasting into the
text box.
Gross - DVD
Revenue
Explanatory variable =
Response variable =
ii) Write down the correlation coefficient and
coefficient of determination
Correlation coefficient = [round answer to 2 decimal
places. Please use a zero (0) before the decimal
point]
Coefficient of determination = [round answer to
4 decimal places. Please use a zero (0) before the
decimal point]
b) Seeing such a low coefficient of determination value, I
immediately wonder why? Maybe there is an outlier in the dataset?
However, it was assumed that all the conditions and assumptions for
inference are satisfied – so what could be the reason? Maybe a
typing error! After carefully examining the dataset, I find a
typing mistake. Instead of typing 53.12 million, the Momma Mia DVD
revenue was accidently typed as 3.12 million.
Correct the value in the dataset and make a scatterplot
again. Determine the coefficient of determination and
interpret its meaning
Coefficient of determination
= [round answer to 4 decimal
places. Please use a zero (0) before the decimal
point]
% of the variation in DVD revenue can be
explained by the variation in box office gross. [round answer
to 2 decimal places]
c) Determine the regression coefficients b0 and
b1. [round answers to 4 decimal places. Please use a
zero (0) before the decimal point of b1]
b0 =
b1 =
d) Interpret the meaning of the slope in this
problem.
For each increase of 1 million dollars of box office gross, the
predicted DVD revenue is estimated to increase by
$ million [round answer to 4 decimal places. Please
use a zero (0) before the decimal point]
e) Predict the sales revenue for a movie DVD that had a
box office gross of $75 million.
Predicted DVD Revenue = $ million [round
answer to 2 decimal places]
f) At 5% level of significance, is there evidence of a
linear relationship between box office gross and DVD
revenue?
NOTE: Copy and paste the following wordings (highlighted
in yellow) into the section below as is
appropriate. Use only the highlighted wordings. Do not
add any extra space or symbol when copying and pasting into the
text box.
1. Hypotheses:
b1 ≠ 0 - β1 = 0
- β1 ≠ 0 - no linear
relationship - b1 = 0 - a
linear relationship
H0: (There is between box
office gross and DVD revenue.)
HA: (There is between box
office gross and DVD revenue.)
2. Test statistic:
t = [round answer to 4
decimal places]
P-value = p-value = [round
answer to 1 decimal place. Please use a zero (0)
before the decimal point]
R2 = [round answer to 4 decimal
places. Please use a zero (0) before the decimal
point]
3. Decision rule:
less than - greater than
- reject H0 - fail to
reject H0 - very good
- good - excellent
- weak
4. Conclusion:
no evidence - strong
evidence
Based on the sample and at 5% level of significance, there
is of a linear relationship between box office gross and
DVD revenue.
g) Construct and interpret 95% and 98% confidence
interval estimates of the population slope of the true
relationship. [round ALL answers to 4 decimal places. Please
use a zero (0) before the decimal point]
95% confidence interval estimate of the population slope =
($ million,
$ million)
For each increase of 1 million dollars of box office gross, we
are 95% confident that the DVD revenue is estimated to increase by
between $ million and
$ million.
98% confidence interval estimate of the population slope =
($ million,
$ million)
For each increase of 1 million dollars of box office gross, we
are 98% confident that the DVD revenue is estimated to increase by
between $ million and
$ million.
previously released only in theatres has the business objective of
developing estimates of the sales revenue of DVDs. Towards this
goal, a company analyst plans to use box office gross to predict
DVD sales revenue. For 22 movies, the analyst collects the box
office gross (in $millions) in the year that they were released and
DVD revenue (in $millions) in the following year. The data are
stored in DVD Revenue.xlsx
For these data, assuming all the conditions and assumptions for
inference are satisfied:
a) Construct a scatterplot.
i) Write down the explanatory variable and response
variable
NOTE: Copy and paste the following wordings (highlighted
in yellow) into the section below as is
appropriate. Use only the highlighted wordings. Do not
add any extra space or symbol when copying and pasting into the
text box.
Gross - DVD
Revenue
Explanatory variable =
Response variable =
ii) Write down the correlation coefficient and
coefficient of determination
Correlation coefficient = [round answer to 2 decimal
places. Please use a zero (0) before the decimal
point]
Coefficient of determination = [round answer to
4 decimal places. Please use a zero (0) before the
decimal point]
b) Seeing such a low coefficient of determination value, I
immediately wonder why? Maybe there is an outlier in the dataset?
However, it was assumed that all the conditions and assumptions for
inference are satisfied – so what could be the reason? Maybe a
typing error! After carefully examining the dataset, I find a
typing mistake. Instead of typing 53.12 million, the Momma Mia DVD
revenue was accidently typed as 3.12 million.
Correct the value in the dataset and make a scatterplot
again. Determine the coefficient of determination and
interpret its meaning
Coefficient of determination
= [round answer to 4 decimal
places. Please use a zero (0) before the decimal
point]
% of the variation in DVD revenue can be
explained by the variation in box office gross. [round answer
to 2 decimal places]
c) Determine the regression coefficients b0 and
b1. [round answers to 4 decimal places. Please use a
zero (0) before the decimal point of b1]
b0 =
b1 =
d) Interpret the meaning of the slope in this
problem.
For each increase of 1 million dollars of box office gross, the
predicted DVD revenue is estimated to increase by
$ million [round answer to 4 decimal places. Please
use a zero (0) before the decimal point]
e) Predict the sales revenue for a movie DVD that had a
box office gross of $75 million.
Predicted DVD Revenue = $ million [round
answer to 2 decimal places]
f) At 5% level of significance, is there evidence of a
linear relationship between box office gross and DVD
revenue?
NOTE: Copy and paste the following wordings (highlighted
in yellow) into the section below as is
appropriate. Use only the highlighted wordings. Do not
add any extra space or symbol when copying and pasting into the
text box.
1. Hypotheses:
b1 ≠ 0 - β1 = 0
- β1 ≠ 0 - no linear
relationship - b1 = 0 - a
linear relationship
H0: (There is between box
office gross and DVD revenue.)
HA: (There is between box
office gross and DVD revenue.)
2. Test statistic:
t = [round answer to 4
decimal places]
P-value = p-value = [round
answer to 1 decimal place. Please use a zero (0)
before the decimal point]
R2 = [round answer to 4 decimal
places. Please use a zero (0) before the decimal
point]
3. Decision rule:
less than - greater than
- reject H0 - fail to
reject H0 - very good
- good - excellent
- weak
4. Conclusion:
no evidence - strong
evidence
Based on the sample and at 5% level of significance, there
is of a linear relationship between box office gross and
DVD revenue.
g) Construct and interpret 95% and 98% confidence
interval estimates of the population slope of the true
relationship. [round ALL answers to 4 decimal places. Please
use a zero (0) before the decimal point]
95% confidence interval estimate of the population slope =
($ million,
$ million)
For each increase of 1 million dollars of box office gross, we
are 95% confident that the DVD revenue is estimated to increase by
between $ million and
$ million.
98% confidence interval estimate of the population slope =
($ million,
$ million)
For each increase of 1 million dollars of box office gross, we
are 98% confident that the DVD revenue is estimated to increase by
between $ million and
$ million.