The table below shows the number of grams of carbohydrates, x, andthe number of Calories, y, of six different foods.
Carbohydrates (x) Calories (y)
8 120
9.5 138
10 147
6 88
7 108
4 62
Which equation best represents the line of best fit for this set of data?
(1) y = 15x (3) y = 0.1x - 0.4
(2) y = 0.07x (4) y = 14.1x + 5.8
Answers
Final answer:
The equation that best represents the line of best fit for the given data set is likely equation (1) y = 15x, as it renders values of y that closely match those in the original table when corresponding x values are substituted.
Explanation:
To determine which equation best represents the line of best fit for the given set of data, we need to find an equation that fits the relationship between the number of grams of carbohydrates (x) and the number of Calories (y).
Looking at the data, it appears that y increases as x increases, indicating a positive linear relationship. In other words, as the number of carbohydrates increase, the number of calories also increase. We can examine this by calculating the ratio of y to x for each pair and check for consistency.
The line of best fit represents this relationship most accurately when the equation provides values that are closest to the actual y values in the table when the corresponding x values are substituted into the equation.
By this criterion, if you substitute the values of x in the equation (1) y = 15x, you'll notice that the values of y you get are very close to those given in the table, making it a strong contender for the line of best fit in this scenario.
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The equation that represents the line of best fit is y = 14.1x + 5.8
Finding the equation that represents the line of best fit
From the question, we have the following parameters that can be used in our computation:
The table of values
Using a graphing tool, we have the following summary
- Sum of X = 44.5
- Sum of Y = 663
- Mean X = 7.4167
- Mean Y = 110.5
- Sum of squares (SSX) = 25.2083
- Sum of products (SP) = 355.75
The regression equation is represented as
y = bx + a
Where
b = SP/SSX = 355.75/25.21 = 14.1
a = MY - bMX = 110.5 - (14.11*7.42) = 5.8
So, we have
y = 14.1x + 5.8
Hence, the equation is y = 14.1x + 5.8
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