Construct a scatterplot and identify the mathematical model that best fits the data. Assume that the model is to be used only for the scope of the given data and consider only linear, quadratic, logarithmic, exponential, and power models. Use a calculator or computer to obtain the regression equation of the model that best fits the data. You may need to fit several models and compare the values of R2.
y = 6.22 e1.39x
y = 20.14 + 13.36 ln x
y = 11.11x0.855
y = 9.56 + 5.66x
Answers
Answer:
i)
Find the attached
ii)
The mathematical model that best fits the data is;
y = 7.19 + 12.8 ln x
Step-by-step explanation:
i)
A scatter-plot can easily be constructed using applications such as Ms. Excel and Stat-Crunch.
In Ms. Excel we first enter the data in any two adjacent columns. Next, highlight the data, then click the insert ribbon and select the scatter-plot option.
Excel returns a scatter-plot chart as shown in the attachment below.
ii)
After obtaining the scatter-plot, we shall need to add a trend line in order to determine the mathematical model that best fits the data given.
Click anywhere inside the chart, then select the design tab under chart tools. Click on the Add Chart element in the upper left corner of the excel workbook and select more trend-line options. This feature will enable us to fit any trend-line to our data.
Select any trend line option ensuring you check the boxes; Display Equation on chart and Display R-squared value on chart.
Find the attached for the various trend-lines.
The mathematical model that best fits the data is;
y = 7.19 + 12.8 ln x
Since it has the largest R-squared value of 0.9905
The regression equation of the table of values is y = 9.56 + 5.66x
How to draw the scatter plot?The table of values is given as:
x: 0.2 0.7 1.9 3.5 7.7
y: 3 5 35 37 47
See attachment for the scatter plot based on the above table of values
How to determine the regression equation?To do this, we make use of a graphing calculator with the following calculation summary:
Sum of X = 14Sum of Y = 127Mean X = 2.8Mean Y = 25.4Sum of squares (SSX) = 36.48Sum of products (SP) = 206.4The regression equation is represented as: y = a + bx
Where
b = SP/SSX = 206.4/36.48 = 5.66
a = MY - bMX = 25.4 - (5.66*2.8) = 9.56
So, we have:
y = 9.56 + 5.66x
Hence, the regression equation of the table of values is y = 9.56 + 5.66x
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