Answer to Question #245099 in Statistics and Probability for mechanix

Question

1. If the mode of a certain frequency table is 𝟔𝟓.𝟓 and the lower limit of the modal class is

𝟔𝟎.𝟓 with the class size 𝟏𝟎, find the frequency of the modal class. Here frequency

difference of the modal class and pre-modal class is 𝟕 and frequency of post-modal class

is 𝟏𝟒.

2. If the correlation coefficient of two variables is 𝟎.𝟔𝟓 and regression coefficient of

𝒚 on 𝒙 is 𝟏. 𝟔𝟖. Also, x̄= 𝟑𝟐. 𝟑 and ȳ = 𝟒𝟓.𝟔.

(i) Find the regression coefficient of 𝒙 on 𝒚.

(ii) Find and sketch the regression line 𝒙 on 𝒚.

(iii) Predict the value of 𝒙 when 𝒚 is 𝟓𝟐. Also, verify your result graphically

3. If the correlation coefficient of 𝒙 & 𝒚 is 𝟎. 𝟕𝟓 and the corresponding standard deviations

𝟏.𝟐𝟓 & 𝟏.𝟕𝟓. Find the regression coefficient of 𝒚 on 𝒙 and 𝒙 on 𝒚.