Question

The table shows the temperature of an amount of water set on a stove to boil, recorded every half minute. a 2-row table with 10 columns. the first row is labeled time (minutes) with entries 0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4, 4.5. the second row is labeled temperature (degrees celsius) with entries 75, 79, 83, 86, 89, 91, 93, 94, 95, 95.5. according to the line of best fit, at what time will the temperature reach 100°c, the boiling point of water? 5 5.5 6 6.5

Answer 1

According to the line of best fit, the value of time when the temperature reach 100°c, the boiling point of water is 5.

What is linear regression?

Linear regression is a type of regression which is used to model the statement in which the growth or decay initially with constant rate, and then slow down with respect to time.

The table shows the temperature of an amount of water set on a stove to boil, recorded every half minute. a 2-row table with 10 columns.

• Time (minutes X)                 0, 0.5,1.0, 1.5, 2.0,2.5,3.0, 3.5, 4,  4.5.
• Temperature (° Celsius Y)  75, 79, 83, 86, 89, 91, 93,  94, 95, 95.5.

The sum of time is 22.5 and the sum of temperature value is 880.5. In this table,

• The mean of time value, 2.25.
• The mean of temperature value 88.05
• Sum of squares 20.625
• Sum of products 93.625

The regression equation for this data can be given as,

$\hat y=4.53939 X+77.83636$

Put the value of temperature (y) 100 in this equation.

$100=4.53939 X+77.83636\\X=\dfrac{100-77.83636}{4.53939}\\X\approx 5$

Hence, according to the line of best fit, the value of time when the temperature reach 100°c, the boiling point of water is 5.

Learn more about the regression here;

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