Question

An art dealer is trying to determine whether the age of a painting plays a significant role in its price at auction. She collects the sale data for 10 paintings, including the painter, the title of the painting, the age of the painting at auction, and the sale at auction (in million $). The data is reproduced in the table below. Calculate the correlation coefficient rusing a TI-83, TI-83 plus, or TI-84 graphing calculator (round your answer to two decimal places).

Artist Title Age at auction (in years) Price sold (in million $)
Peter Paul Rubens Massacre of the Innocents 391 76.7
Roy Lichtenstein Nurse 51 95.4
Francis Bacon Triptych, 1976 32 86.3
Pablo Picasso Les Noces de Pierrette 84 49.3
Jasper Johns False Start 47 80
Vincent van Gogh A Wheatfield with Cypresses 104 57
Pablo Picasso Yo, Picasso 88 47.8
Andy Warhol Turquoise Marilyn 43 80
Titian Portrait of Alfonso d'Avalos 470 70
Mark Rothko Orange, Red, Yellow 51 86.9

Answer 1

-0.20

Explanation:

Given the data:

Age at auction (x) ____price sold (y)

391

51

32

84

47

104

88

43

470

51

Y:

76.9

95.4

86.3

49.3

80

57

47.8

80

70

86.9

General formula for a simple linear regression :

y = ab + c

Where ;

y = predicted variable ; a = slope / gradient

b = predictor / independent variable ; c = intercept

From the result obtained from the calculator :

y = -0.01246X + 74.65552

Correlation Coefficient is used to measure the strength of relationship between linear variables.

The regression Coefficient obtained is - 0.20

This shows that there is a weak negative correlation between the age at auction and the price at which painting is sold. This is because the negative sign means that value of y decreases as x increases or vice versa, however, due to a correlation vale which is closer to 0 than 1 or - 1, we can conclude that the negative relationship between the variables is weak.