Question

The table has data reflecting the measured population of Complete the descriptors of the regression equation for
North Carolina in terms of years since 1920.
this data.
Time (Years)
Population (Millions)
The data is best modeled by
function.
0
15
30
45
60
75
2.58
3.23
4.07
4.86
5.58
7.185
The value of a is
and the value of cis
the value of b is

Answer 1

The function can be best modeled by a linear regression and the values of a, b and c are -6, 100 and 240, respectively

The function type

From the table, we have the following highlight:

• As the number of years increases by 15
• The population increases

Only linear functions behave in the above manner

Hence, the function can be best modeled by a linear regression.

The solution to a, b and c

A linear regression equation can be represented in the following ways

• ax + by = c
• y = mx + b

Start by entering the data in the table in a graphing calculator.

The calculation summary from the graphing calculator is as follows:

• Sum of X = 225
• Sum of Y = 27.505
• Mean X = 37.5
• Mean Y = 4.5842
• Sum of squares (SSX) = 3937.5
• Sum of products (SP) = 231.4875

The regression equation is then represented as:

y = bx + a

Where:

b = SP/SSX = 231.49/3937.5 = 0.05879

a = MY - bMX = 4.58 - (0.06*37.5) = 2.37952

So, we have:

y = 0.05879x + 2.37952

Approximate

y = 0.06x + 2.4

Multiply through by 100

100y = 6x + 240

Rewrite as:

-6x + 100y = 240

Hence, the values of a, b and c are -6, 100 and 240, respectively

Read more about regression equation at:

brainly.com/question/14184702

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