Question

7

A researcher working for the Ray-Ban Corporation decides to perform a hypothesis test to investigate whether there is a significant positive correlation between monthly temperature and number of sunglasses sold at one of their locations. The researcher randomly selected the following sample from this location. Monthly Temperature (°F) Number of Sunglasses Sold 80 91 61 34 56 66 99 72 71 74 95 125 43 65 (TEMP SUMS: 2x = 505; E x2 = 38,973) (NBR SUMS: 2 x = 527; E x2 = 44,303) Using the Regression equation, the predicted the number (to the nearest whole number) of sunglasses sold for a monthly temperature of 50°F is:

Answer 1

X :- Temperature

Y :- Sunglasses sold

ΣX = 505
ΣY = 527
ΣX * Y = 40102
ΣX2 = 38973
ΣY2 = 44303

Equation of regression line is Ŷ = a + bX
$b = ( n \Sigma XY - \Sigma X \Sigma Y) / ( n\Sigma X^{2} - (\Sigma X)^{2})$

b = 0.82
a =( Σ Y - ( b * Σ X) ) / n
a =( 527 - ( 0.8197 * 505 ) ) / 7
a = 16.151
Equation of regression line becomes Ŷ = 16.151 + 0.82 X

When X = 50
Ŷ = 16.151 + 0.82 X
Ŷ = 16.151 + ( 0.82 * 50 )
Ŷ = 57.15