Question

For 50 randomly selected speed​ dates, attractiveness ratings by males of their female date partners​ (x) are recorded along with the attractiveness ratings by females of their male date partners​ (y); the ratings range from 1 to 10. The 50 paired ratings yield x (overboard)= 6.3​, y (overboard) =6.0​, r = −0.275​, ​P-value= 0.053​, and y^ = 8.13−0.332x. Find the best predicted value of

ModifyingAbove y with caret y^ ​(attractiveness rating by female of​ male) for a date in which the attractiveness rating by the male of the female is x = 4. Use a 0.01 significance level.

The best predicted value of y^ when x = 4 is _______.

​(Round to one decimal place as​ needed.)

Answer 1

Let's write the given information.

n = sample size = 50

= 6.3 , = 6.0

coefficient of correlation = r = -0.275

P - value = 0.053

Predicted regression line is

The given level of significance = = 0.01

Consider the following two decision rule:

1 ) If P-value < , then we use predicted regression line to find the best predicted value of y for given value of x.

2 ) If P-value >=   , then we use sample mean of y as the best predicted value of y for any given value of x.

Here p-value = 0.053 > 0.01 = ( ), so we need to use second rule.

So that: The best predicted value of y^ when x = 4 is =   = 6.0 ( This is the final answer).