Question

asked Sep 15, 2021 214k views

1 Answer

Nubm · Answer 1 · 2021-09-20T15:06:55+0000

Answer:

a) Figure attached

b)
y=-6.238 x +952.62

c)
y=-6.238*70 +952.62=515.955

Explanation:

For this case we assume that x= "Ticket price (cents)" and y ="assengers per 100 miles"

X: 25 30 35 40 45 50 55 60

Y: 800 780 780 660 640 600 620 620

Plot these data.

And the plot is on the figure attached. We see a linear inverse relationship between the two variables.

Develop the estimating equation that best describes these data.

We want to estimate a linear model
y =mx+b

For this case we need to calculate the slope with the following formula:

m=(S_(xy))/(S_(xx))

Where:

$S_(xy)=\sum_(i=1)^n x_i y_i -((\sum_(i=1)^n x_i)(\sum_(i=1)^n y_i))/(n)$

$S_(xx)=\sum_(i=1)^n x^2_i -((\sum_(i=1)^n x_i)^2)/(n)$

So we can find the sums like this:

$\sum_(i=1)^n x_i =340$

$\sum_(i=1)^n y_i =5500$

$\sum_(i=1)^n x^2_i =15500$

$\sum_(i=1)^n y^2_i =3830800$

$\sum_(i=1)^n x_i y_i =227200$

With these we can find the sums:

$S_(xx)=\sum_(i=1)^n x^2_i -((\sum_(i=1)^n x_i)^2)/(n)=15500-(340^2)/(8)=1050$

$S_(xy)=\sum_(i=1)^n x_i y_i -((\sum_(i=1)^n x_i)(\sum_(i=1)^n y_i))/(n)=227200-(340*5500)/(8)=-6550$

And the slope would be:

m=-(6550)/(1050)=-6.238

Nowe we can find the means for x and y like this:

$\bar x= (\sum x_i)/(n)=(340)/(8)=42.5$

$\bar y= (\sum y_i)/(n)=(5500)/(8)=687.5$

And we can find the intercept using this:

$b=\bar y -m \bar x=687.5-(-6.238*42.5)=952.62$

So the line would be given by:

y=-6.238 x +952.62

Predict the number of passengers per 100 miles if the ticket price were 70 cents.

For this case we just need to replace x=70 in our model and we got:

y=-6.238*70 +952.62=515.955

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