6 observations on (X ,Y) yielded the following data:i) Determi

Question

6 observations on (X ,Y) yielded the following data:

$\sum X_{i}=30,\quad\sum Y_{i}=180,\quad\sum X_{i}Y_{i}=1000,\\\sum X_{i}^{2}=200,\quad\sum Y_{i}^{2}=5642.$

i) Determine the correlation coefficient between X and Y.

ii) Given X =10, what will be the predicted value of Y ?

iii) Given Y =15,what will be the predicted value of X ?

18 Feb 2025

Answer :

Word Count : 346

We will solve this step by step. ### Given Data: \[ \sum X_i = 30, \quad \sum Y_i = 180, \quad \sum X_i Y_i = 1000 \] \[ \sum X_i^2 = 200, \quad \sum Y_i^2 = 5642 \] Number of observations: $ n = 6 $ ### Step 1: Compute Means \[ \bar{X} = \frac{\sum X_i}{n} = \frac{30}{6} = 5 \] \[ \bar{Y} = \frac{\sum Y_i}{n} = \frac{180}{6} = ________ ________ ______ _____ __________ ________ ___ _______ _______ ________ _____.
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