Question

What is the critical value for the linear correlation coefficient, r, for a sample of size n = 15 with α = .01 ? (Round to the nearest thousandth.

The linear correlation coefficient for a set of paired variables is r = .897. What proportion of the variation in y can be explained by the linear relationship between x and y? (Type the percentage rounded to the nearest hundredth without the % sign.

The linear regression equation for a set of data is ŷ = 2.3x₀ + 5 . The value of ȳ for this data set is 10.1 , and n = 10 . Use α = .05 . If the linear correlation coefficient for this data is r = .521 , what is the best y-value for x = 5 ? (Round to the nearest tenth.

The linear regression equation for a set of data is ŷ = 2.3x₀ + 5 . The value of ȳ for this data set is 10.1 , and n = 10 . Use α = .05 . If the linear correlation coefficient for this data is r = .972 , what is the best y-value for x = 5 ?

Answer 1

1) What is the critical value for the linear correlation coefficient, r, for a sample of size n = 15 with α = .01 ?

Critical value = 0.641 ---( from r table )

2) The linear correlation coefficient for a set of paired variables is r = .897. What proportion of the variation in y can be explained by the linear relationship between x and y? (Type the percentage rounded to the nearest hundredth without the % sign.

r² = 80.46

3)The linear regression equation for a set of data is y = 2.3x₀ + 5 . The value of y bar for this data set is 10.1 , and n = 10 . Use α = .05 . If the linear correlation coefficient for this data is r = .521 , what is the best y-value for x = 5 ? (Round to the nearest tenth.)

Critical value = 0.632 , | r | = 0.521

As | r | is less than critical value , there is no significant correlation exists between x and y

So we have to use y bar as best predicted value of y

Answer = 10.1

4)The linear regression equation for a set of data is yy = 2.3x₀ + 5 . The value of y bar for this data set is 10.1 , and n = 10 . Use α = .05 . If the linear correlation coefficient for this data is r = .972 , what is the best y-value for x = 5 ?

Critical value = 0.632 , | r | = 0.972

As | r | is greater than critical value , there is significant correlation exists between x and y

So we can use regression equation to predict the y

y = (2.3*5) + 5

Answer = 16.5