Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
4th Edition
ISBN: 9780133178579
Author: Ross L. Finney
Publisher: PEARSON
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Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
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Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as p…
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Chapter 1.2, Problem 54E

(a)

To determine

To find:The quadratic regressionfor the datagiven in the table for the gross revenue of Broadway season.

(a)

Expert Solution
Check Mark

Answer to Problem 54E

The quadratic regression equation for the given data ofBroadway Season Revenue is y=0.723x2+26.726x+290.914 .

Explanation of Solution

Given information:The table given below shows the gross revenue for Broadway season in different years:

    Broadway Season Revenue
    YearAmount ($ millions)
    1994406
    1999603
    2004769
    2005862
    2006939
    2007938

Calculation:

Consider that x=0 represents year 1999, x=1 represents year 2000, x=2 represents year 2001 and so on.

To find the natural logarithm regression equation of the given data, use graphing calculator.

Step 1: Press STAT1 keys to enter the given data.

Step 2: List the input values 4, 9, 14, 15, 16 and 17 in the L1 column.

Step 3: List the input values 406, 603, 769, 862, 939 and 938 in the L2 column.

Step 4: Press the keystrokes STAT⇒5ENTER to find line of quadratic regression and again press ENTER key.

  y=0.723x2+26.73+290.914

Therefore, the quadratic regression equation for the Broadway Season Revenue is y=0.723x2+26.726x+290.914 .

(b)

To determine

To plot:The graph of the quadratic regression for the given data on a scatter plot.

(b)

Expert Solution
Check Mark

Explanation of Solution

Given information:The table given below shows the gross revenue for Broadway season in different years:

    Broadway Season Revenue
    YearAmount ($ millions)
    1994406
    1999603
    2004769
    2005862
    2006939
    2007938

Graph:

From part (a), the quadratic regression equation for the Broadway Season Revenue is y=0.723x2+26.726x+290.914 . Now, to make the scatter plot, follow the steps using graphing calculator.

Step 1: Press 2ndY= and make sure that Plot 1 is ON. Choose the scatter plot icon in type.

Step 2: Press GRAPH key. Set the window at [0, 20] by [300, 1000] .

Step 3: Press the keystrokes STAT⇒5ENTER2nd1,2nd2,VARS⇒11ENTER and. Now, press the GRAPH key to plot the graph as shown below.

  Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy), Chapter 1.2, Problem 54E

Figure (1)

Interpretation: From the graph it can be observed that the gross revenue for Broadway season in year 2008 is more than 1000 millions of dollars.

(c)

To determine

To find: The amount of gross revenue for the Broadway Season in year 2012.

(c)

Expert Solution
Check Mark

Answer to Problem 54E

The amount of gross revenue for the Broadway Season in year 2012 is 1228.15 millions of dollars.

Explanation of Solution

Given information:The table given below shows the gross revenue for Broadway season in different years:

    Broadway Season Revenue
    YearAmount ($ millions)
    1994406
    1999603
    2004769
    2005862
    2006939
    2007938

Calculation:

From part (a), the quadratic regression equation for the Broadway Season Revenue is y=0.723x2+26.726x+290.914 .

Consider that x=0 represents year 1999, x=1 represents year 2000, x=2 represents year 2001, x=17 represents year 2007and so on. The year 2012 is represented by x=22 .

Substitute 22 for x in the quadratic regression equation.

  y=0.723(22)2+26.73(22)+290.914y=1228.15

Therefore, the amount of gross revenue for the Broadway Season in year 2012 is 1228.15 millions of dollars.

(d)

To determine

To find:The linear regression for the data given in the table for the gross revenue of Broadway season and the amount of revenue in 2012.

(d)

Expert Solution
Check Mark

Answer to Problem 54E

The linear regression equation for the Broadway Season Revenue is y=41.87x+229.48 and the approximate revenue in year 2012 is $1150 million.

Explanation of Solution

Given information:The table given below shows the gross revenue for Broadway season in different years:

    Broadway Season Revenue
    YearAmount ($ millions)
    1994406
    1999603
    2004769
    2005862
    2006939
    2007938

Calculation:

To find the linear regression equation of the given data, use graphing calculator.

Press the keystrokes STAT⇒4ENTER .

  y=41.87x+229.48

Now, substitute 22 for x in the above equation to find the revenue in 2012.

  y=41.87(22)+229.48y=1150.62

Therefore, the linear regression equation for the Broadway Season Revenue is y=41.87x+229.48 and the approximate revenue in year 2012 is $1150 million.

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Chapter 1.2, Problem 53E
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Chapter 1.2, Problem 55E

Chapter 1 Solutions

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

Ch. 1.1 - Prob. 1QRCh. 1.1 - Prob. 2QRCh. 1.1 - Prob. 3QRCh. 1.1 - Prob. 4QRCh. 1.1 - Prob. 5QRCh. 1.1 - Prob. 6QRCh. 1.1 - Prob. 7QRCh. 1.1 - Prob. 8QRCh. 1.1 - Prob. 9QRCh. 1.1 - Prob. 10QR
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Prob. 30ECh. 1.6 - Prob. 31ECh. 1.6 - Prob. 32ECh. 1.6 - Prob. 33ECh. 1.6 - Prob. 34ECh. 1.6 - Prob. 35ECh. 1.6 - Prob. 36ECh. 1.6 - Prob. 37ECh. 1.6 - Prob. 38ECh. 1.6 - Prob. 39ECh. 1.6 - Prob. 40ECh. 1.6 - Prob. 41ECh. 1.6 - Prob. 42ECh. 1.6 - Prob. 43ECh. 1.6 - Prob. 44ECh. 1.6 - Prob. 45ECh. 1.6 - Prob. 46ECh. 1.6 - Prob. 47ECh. 1.6 - Prob. 48ECh. 1.6 - Prob. 49ECh. 1.6 - Prob. 50ECh. 1.6 - Prob. 51ECh. 1.6 - Prob. 52ECh. 1.6 - Prob. 53ECh. 1.6 - Prob. 54ECh. 1.6 - Prob. 55ECh. 1.6 - Prob. 56ECh. 1.6 - Prob. 57ECh. 1.6 - Prob. 58ECh. 1.6 - Prob. 59ECh. 1.6 - Prob. 60ECh. 1.6 - Prob. 61ECh. 1.6 - Prob. 62ECh. 1.6 - Prob. 1QQCh. 1.6 - Prob. 2QQCh. 1.6 - Prob. 3QQCh. 1.6 - Prob. 4QQCh. 1 - Prob. 1RECh. 1 - Prob. 2RECh. 1 - Prob. 3RECh. 1 - Prob. 4RECh. 1 - Prob. 5RECh. 1 - Prob. 6RECh. 1 - Prob. 7RECh. 1 - Prob. 8RECh. 1 - Prob. 9RECh. 1 - Prob. 10RECh. 1 - Prob. 11RECh. 1 - Prob. 12RECh. 1 - Prob. 13RECh. 1 - Prob. 14RECh. 1 - Prob. 15RECh. 1 - Prob. 16RECh. 1 - Prob. 17RECh. 1 - Prob. 18RECh. 1 - Prob. 19RECh. 1 - Prob. 20RECh. 1 - Prob. 21RECh. 1 - Prob. 22RECh. 1 - Prob. 23RECh. 1 - Prob. 24RECh. 1 - Prob. 25RECh. 1 - Prob. 26RECh. 1 - Prob. 27RECh. 1 - Prob. 28RECh. 1 - Prob. 29RECh. 1 - Prob. 30RECh. 1 - Prob. 31RECh. 1 - Prob. 32RECh. 1 - Prob. 33RECh. 1 - Prob. 34RECh. 1 - Prob. 35RECh. 1 - Prob. 36RECh. 1 - Prob. 37RECh. 1 - Prob. 38RECh. 1 - Prob. 39RECh. 1 - Prob. 40RECh. 1 - Prob. 41RECh. 1 - Prob. 42RECh. 1 - Prob. 43RECh. 1 - Prob. 44RECh. 1 - Prob. 45RECh. 1 - Prob. 46RECh. 1 - Prob. 47RECh. 1 - Prob. 48RECh. 1 - Prob. 49RECh. 1 - Prob. 50RECh. 1 - Prob. 51RECh. 1 - Prob. 52RECh. 1 - Prob. 53RECh. 1 - Prob. 54RECh. 1 - Prob. 55RECh. 1 - Prob. 56RECh. 1 - Prob. 57RECh. 1 - Prob. 58RECh. 1 - Prob. 59RECh. 1 - Prob. 60RECh. 1 - Prob. 61RECh. 1 - Prob. 62RECh. 1 - Prob. 63RECh. 1 - Prob. 64RECh. 1 - Prob. 65RECh. 1 - Prob. 66RECh. 1 - Prob. 67RECh. 1 - Prob. 68RECh. 1 - Prob. 69RECh. 1 - Prob. 70RE

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