Question

- Linear Regression and Correlation Kamal Hamid 15 You run a regression analysis on a bivariate set of data (n 73). You obtain the regression equation = 1.5422+-1.366 with a correlation coefficient of r = 0.45 (which is signifi average) for the explanatory variable will give you a value of 80 on the res cant at α = 0.01). You want to predict what value (on What is the predicted explanatory value?

Answer 1

#1 )  

We are given regression equation :

y = 1.542x - 1.366

Therefore , x =  $\frac{y + 1.366}{1.542}$

We are given value of response variable y = 80 and asked to find x

x = $\frac{80+ 1.366}{1.542}$

x = 52.7665  

( Please round the value of x to given specific decimal places )

#2 ) First we need to find correlation coefficient r for the given data set , we can use excel function =CORREL (x,y) to find the value of r

Therefore correlation coefficient r = 0.9688

To check the significance of correlation we have to perform correlation test .

H₀ : The significant correlation exists between X and Y

H_a : The significant correlation does not exists between X and Y

Test statistic : r = 0.9688

Critical value : We are given  $\alpha$ = 0.05, and we have n = number of pairs of x and y = 13

Critical value = 0.553

Decision rule :

If correlation coefficient r is greater than critical value , there is significant correlation exists.

If correlation coefficient r is less than critical value , there is no significant correlation exists.

Here r = 0.9688 and critical value = 0.553

As r is greater than critical value , there is significant correlation exists between the X and Y

Now we have to find the regression equation Y = ax + b

a is slope and b is intercept of the equation.

We can use excel function =SLOPE(Y,X) and =INTERCEPT(Y,X) to find slope a and intercept b respectively.

Therefore slope a = 0.5272 and intercept b = 29.6225

The regression equation is Y = 0.5272X + 29.6225

X = $\frac{y - 29.6225}{0.5272}$

We are given Y = 24.2 and asked to find X

X = $\frac{24.2 - 29.6225}{0.5272}$

X = -10.3