The equations of two regression lines are given as follows:
Calculate (i) regression coefficients, and
; (ii) correlation coefficient r(x, y); (iii) Mean of X and Y; and (iv) the value of
if
.
To solve this problem, we'll first rewrite the given equations in the slope-intercept form (y = mx + c), where m is the slope and c is the y-intercept.
Given equations:
1. \(4x - 5y + 30 = 0\)
\(5y = 4x + 30\)
\(y = \frac{4}{5}x + 6\)
2. \(20x - 9y - 107 = 0\)
\(9y = 20x - 107\)
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State whether the following statements are True or False and also give the reason in support of your answer.
a) If standard deviation of x is 5, standard deviation of y = 2x–3 is 7.
b) Mean deviation is least when calculated from the median.
c) The correlation coefficient between x and (a – x) is –1.
d) The regression coefficients byx and bxy of a data are 1.2 and 0.8, respectively.
e) If (AB) = 10, (αB) = 15, (Aβ) = 20 and (αβ) = 30 then A and B are associated.
Fit an exponential curve of the form to the following data:
| X: | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | ||||||
| Y: | 1.0 | 1.2 | 1.8 | 2.5 | 3.6 | 4.7 | 6.6 | 9.1 | ||||||
A researcher collects the following information for two variables x and y: n = 20, r = 0.5, mean (x) = 15, mean (y) = 20, and
Later it was found that one pair of values (x, y) has been wrongly taken as (16, 30) whereas the correct values were (26, 35). Find the correct value of r(x, y)
Find the missing information from the following data:
| Group I | Group II | Group III | Combined | ||
| Number | 50 | ? | 90 | 200 | |
| Standard Deviation | 6 | 7 | ? | 7.746 | |
| Mean | 113 | ? | 115 | 116 | |
If a, b, c, d are constants, then show that the coefficient of correlation between ax+b and cy+d is numerically equal to that between x and y.
If AM and GM of two numbers are 30 and 18, respectively, find the numbers.
The equations of two regression lines are given as follows:
Calculate (i) regression coefficients, and
; (ii) correlation coefficient r(x, y); (iii) Mean of X and Y; and (iv) the value of
if
.