Question

In: Statistics and Probability

Classified ads in a newspaper offered several used toyota corollas for sale. Listed below are the...

  1. Classified ads in a newspaper offered several used toyota corollas for sale. Listed below are the ages of the cars and the advertised prices.

Age (yrs)

Price

1

$        13,990

1

$        13,495

3

$        12,999

4

$          9,500

4

$        10,495

5

$          8,995

5

$          9,295

6

$          6,999

7

$          6,950

7

$          7,850

8

$          6,999

8

$          5,995

10

$          4,950

10

$          4,495

13

$          2,850

  1. Make a scatterplot of the data. Do you think a linear model is appropriate? Explain. (1 point)
  2. Find the equation of the regression line. (use the data analysis tool in excel) (1 Point)
  3. Explain the meaning of the 95% confidence interval for the coefficient of the slope. (1 point)
  4. Based on your model, what is the predicted price for a 9 year old Toyota Corolla? What is the 95% confidence interval and 95% prediction interval?(3 point)

Solutions

Expert Solution

Part a)

Part b)

Regression output confidence interval
variables coefficients std. error    t (df=13) p-value 95% lower 95% upper std. coeff.
Intercept 14,263.9115 449.5861 31.727 1.06E-13 13,292.6397 15,235.1833 0.000
X -957.6269 64.7127 -14.798 1.63E-09 -1,097.4301 -817.8237 -0.9720

Equation of regression line becomes Ŷ = 14263.9115 + -957.6269 X

part c)

We are 95% confident that the true value of slope will lies within the interval ( 13292.64 , 15235.2 ).

Part d)

Predicted values for: Y
95% Confidence Interval 95% Prediction Interval
X Predicted lower upper lower upper Leverage
9 5,645.270 5,038.024 6,252.516 3,776.921 7,513.618 0.118

orchestra answered 1 year ago
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