rebecca16spears
Answered

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The data shown in the table below represents the number of quarters Maria's aunt gives her every year for her birthday.

Age (in years) Number of quarters
2 32
6 47
7 51
4 40
5 43
3 38
8 60
1 23

Part A: Create a scatter plot to represent the data shown above. Sketch the line of best fit. Label at least three specific points on the graph that the line passes through. Also include the correct labels on the x-axis and y-axis.
Part B: Algebraically write the equation of the best fit line in slope-intercept form. Include all of your calculations in your final answer.
Part C: Use the equation for the line of best fit to approximate the number of quarters that Maria will be given when she turns 14 years old.

Sagot :

MrRoyal

The equation of the line of best fit is y = 4.57x + 21.19 and Maria will be given 85 quarters at 14 years old

The scatter plot of the data

See attachment

The equation of the line of best fit

From the graphing calculator, we have the following summary;

  • Sum of X = 36
  • Sum of Y = 334
  • Mean X = 4.5
  • Mean Y = 41.75
  • Sum of squares (SSX) = 42
  • Sum of products (SP) = 192

The equation of the line of best fit is represented as:

y = bx + a

Where

b = SP/SSX = 192/42 = 4.57143

a = MY - bMX = 41.75 - (4.57*4.5) = 21.17857

So, we have:

y = 4.57143x + 21.17857

Approximate

y = 4.57x + 21.19

Hence, the equation of the line of best fit is y = 4.57x + 21.19

The number of quarters at 14 years old

This means that:

x = 14

So, we have

y = 4.57 * 14 + 21.19

Evaluate

y = 85.17

Approximate

y = 85

Hence, Maria will be given 85 quarters at 14 years old

Read more about regression at:

https://brainly.com/question/25987747

#SPJ1

View image MrRoyal
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