a. Answer Explanation Given information: The table of values given is as follows: Year (x) Personal income in dollar (y) 1995 23255 1996 24270 1997 25412 1998 26893 1999 27880 2000 29760 2001 30413 2002 30832 2010 ? Calculation: The graph for the given data is shown below. b. To determine To find: best fit line using two ordered pairs. Answer y = 1084 x − 2139336 Explanation Given information: The table of values given is as follows: Year (x) Personal income in dollar (y) 1995 23255 1996 24270 1997 25412 1998 26893 1999 27880 2000 29760 2001 30413 2002 30832 2010 ? Calculation: Let’s select any two ordered pair like ( 1997 , 25412 ) and ( 2002 , 30832 ) . Plug in the values in the slope equation and solve m as follows: m = y 2 − y 1 x 2 − x 1 = 30832 − 25412 2002 − 1997 = 5420 5 = 1084 Now, plug the value of m and any one point coordinate into the slope intercept equation and evaluate b as follows: y = m x + b 25412 = ( 1084 ) ( 1997 ) + b 25412 = 2164748 + b b = 25412 − 2164748 = − 2139336 Now, plug the values of m and b in the slope intercept formula as follows: y = m x + b y = 1084 x − 2139336 Thus, the line equation is y = 1084 x − 2139336 . c. To determine To find: the equation for regression line and correlation value using the graphing calculator. Answer y = 1164.1071428571 x − 2299128.75 r = 0.9921999084378 Explanation Given information: The table of values given is as follows: Year (x) Personal income in dollar (y) 1995 23255 1996 24270 1997 25412 1998 26893 1999 27880 2000 29760 2001 30413 2002 30832 2010 ? Calculation: The graph for the above equation is as follows: Using the graphing calculator, the regression line equation is as follows: y = 1164.1071428571 x − 2299128.75 Using the graphing calculator, the correlation coefficient comes out to be, r = 0.9921999084378 d. To determine To find: the missing value if regression line equation has strong or moderate relationship, and explains whether the prediction is reliable. Answer ≈ 40726 Prediction is reliable. Explanation Given information: The table of values given is as follows: Year (x) Personal income in dollar (y) 1995 23255 1996 24270 1997 25412 1998 26893 1999 27880 2000 29760 2001 30413 2002 30832 2010 ? y = 1164.1071428571 x − 2299128.75 r = 0.9921999084378 Calculation: The equation of regression line shows strong relationship because 0.75 ≤ r ≤ 1 . Plugging x = 2010 into the regression formula and evaluate y as follows: y = 1164.1071428571 x − 2299128.75 y = 1164.1071428571 ( 2010 ) − 2299128.75 = 2339855 .357142771 − 2299128.75 = 40726.60714277066 ≈ 4076 The regression line represents that the rate of increase in personal income per year is slower than that of inflation. On average, money doubles every seven years. As minimum wage does not increase quickly as compared to inflation and only a small fraction of the population has the large amount of money. So, this data seems reliable and the predicted value is also reliable.

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

1st Edition

ISBN: 9780078682278

Author: McGraw-Hill, Berchie Holliday

Publisher: Glencoe/McGraw-Hill

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Correlation

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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.

Regression Analysis

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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Compare Compare Correlation is the measure of the degree of the relationship between the variables. In regression, the relationship between the variables to predict one by another is assessed. In correlation there is no cause and effect between the variables, whereas in regression there is a cause and effect between the variables. By using correlation, we cannot predict anything, but regression is a predictive tool. Coefficients are symmetrical in correlation but in regression they are asymmetrical. Correlation is independent of change in origin and scale, but regression is not independent of change in scale.

Chapter 1.6, Problem 7E

To determine

To graph: the data on the scatter plot.

Expert Solution

Answer to Problem 7E

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 1.6, Problem 7E , additional homework tip 1

Explanation of Solution

Given information:

The table of values given is as follows:

Year (x)	Personal income in dollar (y)
1995	23255
1996	24270
1997	25412
1998	26893
1999	27880
2000	29760
2001	30413
2002	30832
2010	?

Calculation:

The graph for the given data is shown below.

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 1.6, Problem 7E , additional homework tip 2

To determine

To find: best fit line using two ordered pairs.

Expert Solution

Answer to Problem 7E

y=1084x−2139336

Explanation of Solution

Given information:

The table of values given is as follows:

Year (x)	Personal income in dollar (y)
1995	23255
1996	24270
1997	25412
1998	26893
1999	27880
2000	29760
2001	30413
2002	30832
2010	?

Calculation:

Let’s select any two ordered pair like (1997,25412) and (2002,30832) . Plug in the values in the slope equation and solve m as follows:

m=y2−y1x2−x1=30832−254122002−1997=54205=1084

Now, plug the value of m and any one point coordinate into the slope intercept equation and evaluate b as follows:

y=mx+b25412=(1084)(1997)+b25412=2164748+bb=25412−2164748=−2139336

Now, plug the values of m and b in the slope intercept formula as follows:

y=mx+by=1084x−2139336

Thus, the line equation is y=1084x−2139336 .

To determine

To find: the equation for regression line and correlation value using the graphing calculator.

Expert Solution

Answer to Problem 7E

y=1164.1071428571x−2299128.75r=0.9921999084378

Explanation of Solution

Given information:

The table of values given is as follows:

Year (x)	Personal income in dollar (y)
1995	23255
1996	24270
1997	25412
1998	26893
1999	27880
2000	29760
2001	30413
2002	30832
2010	?

Calculation:

The graph for the above equation is as follows:

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 1.6, Problem 7E , additional homework tip 3

Using the graphing calculator, the regression line equation is as follows:

y=1164.1071428571x−2299128.75

Using the graphing calculator, the correlation coefficient comes out to be, r=0.9921999084378

To determine

To find: the missing value if regression line equation has strong or moderate relationship, and explains whether the prediction is reliable.

Expert Solution

Answer to Problem 7E

≈40726

Prediction is reliable.

Explanation of Solution

Given information:

The table of values given is as follows:

Year (x)	Personal income in dollar (y)
1995	23255
1996	24270
1997	25412
1998	26893
1999	27880
2000	29760
2001	30413
2002	30832
2010	?

y=1164.1071428571x−2299128.75r=0.9921999084378

Calculation:

The equation of regression line shows strong relationship because 0.75≤r≤1 .

Plugging x=2010 into the regression formula and evaluate y as follows:

y=1164.1071428571x−2299128.75 y=1164.1071428571(2010)−2299128.75=2339855.357142771−2299128.75=40726.60714277066≈4076

The regression line represents that the rate of increase in personal income per year is slower than that of inflation. On average, money doubles every seven years. As minimum wage does not increase quickly as compared to inflation and only a small fraction of the population has the large amount of money. So, this data seems reliable and the predicted value is also reliable.

Chapter 1.6, Problem 6E

Chapter 1.6, Problem 8E

Chapter 1 Solutions

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

Ch. 1.1 - Prob. 1CFU Ch. 1.1 - Prob. 2CFU Ch. 1.1 - Prob. 3CFU Ch. 1.1 - Prob. 4CFU Ch. 1.1 - Prob. 5CFU Ch. 1.1 - Prob. 6CFU Ch. 1.1 - Prob. 7CFU Ch. 1.1 - Prob. 8CFU Ch. 1.1 - Prob. 9CFU Ch. 1.1 - Prob. 10CFU

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