HSC Commerce इयत्ता ११ - Tamil Nadu Board of Secondary Education Question Bank Solutions for Business Mathematics and Statistics

A survey was conducted to study the relationship between expenditure on accommodation (X) and expenditure on Food and Entertainment (Y) and the following results were obtained:

Write down the regression equation and estimate the expenditure on Food and Entertainment, if the expenditure on accommodation is ₹ 200.

For 5 observations of pairs of (X, Y) of variables X and Y the following results are obtained. ∑X = 15, ∑Y = 25, ∑X² = 55, ∑Y² = 135, ∑XY = 83. Find the equation of the lines of regression and estimate the values of X and Y if Y = 8; X = 12.

The two regression lines were found to be 4X – 5Y + 33 = 0 and 20X – 9Y – 107 = 0. Find the mean values and coefficient of correlation between X and Y.

The equations of two lines of regression obtained in a correlation analysis are the following 2X = 8 – 3Y and 2Y = 5 – X. Obtain the value of the regression coefficients and correlation coefficients.

The regression coefficient of X on Y

The regression coefficient of Y on X

When one regression coefficient is negative, the other would be

If X and Y are two variates, there can be at most

The lines of regression of X on Y estimates

If the regression coefficient of Y on X is 2, then the regression coefficient of X on Y is

The lines of regression intersect at the point

The term regression was introduced by

Express the following as the sum or difference of sine or cosine:

`sin  "A"/8  sin  (3"A")/8`

Express the following as the sum or difference of sine or cosine:

cos(60° + A) sin(120° + A)

Express the following as the sum or difference of sine or cosine:

`cos  (7"A")/3 sin  (5"A")/3`

Express the following as the sum or difference of sine or cosine:

cos 7θ sin 3θ

Express the following as the product of sine and cosine.

sin A + sin 2A

Express the following as the product of sine and cosine.

cos 2A + cos 4A

Express the following as the product of sine and cosine.

sin 6θ – sin 2θ

Express the following as the product of sine and cosine.

cos 2θ – cos θ