Concept explainers
a.
To draw:
a.
![Check Mark](/static/check-mark.png)
Explanation of Solution
Given:
Following data is given in the form of a table
Graph:
By using the above data, scatter plot is drawn.
Interpretation:
The graph shows that average ticket price has been consistently on the rise.
b.
To find: a linear model using regression utility for the given data and identify the coefficient of determination.
b.
![Check Mark](/static/check-mark.png)
Explanation of Solution
Given:
Following data is given in the form of a table
Graph:
Interpretation:
The given graph shows an almost similar increase according to the linear model.
Here, there are 3 points which lying on the line, thus indicating certain accuracy.
The coefficient of determination is
c.
To find: a linear model with the scatter plot from part (a).
c.
![Check Mark](/static/check-mark.png)
Explanation of Solution
Given:
Following data is given in the form of a table
Graph:
Interpretation:
The given graph shows an almost similar increase according to the linear model.
Here, there are 3 points which lying on the line, thus indicating certain accuracy.
d.
To find: a quadratic model using regression utility for the given data and its coefficient of determination.
d.
![Check Mark](/static/check-mark.png)
Explanation of Solution
Given:
Following data is given in the form of a table
Graph:
Interpretation:
The given graph shows that the curve moves almost similar to the quadratic model. Also there are 4 point lying on the quadratic model thus indicating a comparatively higher accuracy as compared to linear model.
The coefficient of determination is
e.
To find: a quadratic model for the given data.
e.
![Check Mark](/static/check-mark.png)
Explanation of Solution
Given:
Following data is given in the form of a table
Graph:
Interpretation:
The given graph shows that the curve moves almost similar to the quadratic model. Also there are 4 point lying on the quadratic model thus indicating a comparatively higher accuracy as compared to linear model
f.
To find: a better model fit for the data.
f.
![Check Mark](/static/check-mark.png)
Explanation of Solution
Given:
Following data is given in the form of a table
On observation of linear model and the quadratic model, it can be easily said that the quadratic models is better as it closely follows the actual movement of the graph.
This is not true in the case of linear model where only 3 of the points lie on the line as compared to 4 in case of quadratic model.
Conclusion:
Quadratic model is better fit for the data given as the difference between two consecutive values is not constant.
g.
To find: the year when the average movie ticket price is $10.25 using quadratic model.
g.
![Check Mark](/static/check-mark.png)
Explanation of Solution
Given:
Following data is given in the form of a table
Graph:
Interpretation:
Observing the quadratic model, it can be said that the average movie ticket price will be $10.25 in year
Conclusion:
The given data follows a similar pattern to the quadratic model.
This helps in finding the time when the graph will have certain value in the future.
Chapter 2 Solutions
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
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