Question

The total amounts of rainfall at various points in time during a thunderstorm are shown in the table. According to a regression calculator, what is the equation of the line of best fit for the data

Answer 1

^Y= 0.03 + 0.59Xi; r= 0.9979

Explanation:

Hello!

Given the variables:

Y: Rainfall in cm

X: Time in hours.

The estimated regression line is:

^Y= a + bX

a= Y[bar]-bX[bar]

`b= (sumXY-((sumX)(sumY))/(n) )/([sumX^2-((sumX)^2)/(n) ])`

∑X= 15.70; ∑X²= 53.07; ∑Y= 9.50; ∑Y²= 19.29; ∑XY= 31.98

n= 6; X[bar]= 2.62; Y[bar]= 1.58

`b= (31.98-(15.70*9.50)/(6) )/([53.07-((15.70)^2)/(6) ])= 0.59`

a= 1.58-0.59*2.62= 0.03

And the correlation coefficient:

`r= \frac{sumXY-((sumX)(sumY))/(n) }{\sqrt{[sumX^2-((sumX)^2)/(n) ][sumY^2-((sumY)^2)/(n) ]} } = \frac{31.98-(15.70*9.50)/(6) }{\sqrt{[53.07-((15.70)^2)/(6) ][19.29-((9.50)^2)/(6) ]} } = 0.9979`

I hope this help!

Full text

The total amounts of rainfall at various points in time during a thunderstorm are shown in the table.

Rainfall During a Thunderstorm

Time (hours)

0.4

1.1

2.9

3.2

3.7

4.4

Rainfall (cm)

0.3

0.6

1.8

2.0

2.2

2.6

According to a regression calculator, what is the equation of the line of best fit for the data?

A calculator screen. A 2-column table with 6 rows titled Data. Column 1 is labeled x with entries 0.4, 1.1, 2.9, 3.2, 3.7, 4.4. Column 2 is labeled y with entries 0.3, 0.6, 1.8, 2, 2.2, 2.6. The linear regression equation is y almost-equals 0.594 x + 0.029; r almost-equals 0.998.

y almost-equals 0.06 x + 0.03

y almost-equals 0.06 x + 0.29

y almost-equals 0.59 x + 0.03

y almost-equals 0.59 x + 0.29