The equation used to predict how long a cold will last is ŷ=-1.8 + 0.09x1 + 3.2x2 – 1.9x3, where x1is person’s temperature on the first day, x2 is number of people seen each day, and x3 is the amount of sleep the person gets. Use this equation to predict how long a cold will last with a temperature of 101.4 degrees, an average of 4 people seen each day, and 6 hours of sleep.8.7 days10.5 days9.7 days9.5 days

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Mathematics

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The equation used to predict how long a cold will last is ŷ=-1.8 + 0.09x1 + 3.2x2 – 1.9x3, where x1is person’s temperature on the first day, x2 is number of people seen each day, and x3 is the amount of sleep the person gets. Use this equation to predict how long a cold will last with a temperature of 101.4 degrees, an average of 4 people seen each day, and 6 hours of sleep.8.7 days10.5 days9.7 days9.5 days

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DeronE120998go DeronE120998go · Answer 1

Hello there. To solve this question, we have to evaluate the function for each variable.

Given the equation

[tex]\hat{y}=-1.8+0.09x_1+3.2x_2-1.9x_3[/tex]

Where x1 is the person's temperature on the first day, x2 is the number of people seen each day and x3 is the amount of sleep the person gets.

We want to determine how long will this cold last if the person's temperature is 101.4 degrees, has seen an average of 4 people each day and sleeps 6 hours at night.

For this, we simply have to plug the values:

[tex]\begin{gathered} x_1=101.4\,^{\circ}F \\ x_2=4 \\ x_3=6 \end{gathered}[/tex]

Such that we find

[tex]\hat{y}=-1.8+0.09\cdot101.4+3.2\cdot4-1.9\cdot6[/tex]

Multiplying and adding the values gives

[tex]\hat{y}=8.72[/tex]

So we find that the approximate time this cold will last is equal to

[tex]8.7\text{ days}[/tex]