Bus Stat

(a)

(i) The amount of sales for the year (X) should be treated as predictor variable and the annual salary (Y) as the response variable. Predictor variable is used to predict another variable while response variable depends on another variable. The amount of sales (X) can predict the result of annual salary (Y) while Y will be effected depends on X.

(ii)

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(iii) According to the scatter plot, it shown when the amount of sales increases, the salary of manager rises as well. There appears to be a positive linear relationship between amount of sales and salary of manager, but not perfect. Besides, the data points are all close to the line of best fit.

(b)

(i) Y=β0+β1X

X is the independent variable and Y is the predicted value of y corresponding to a given X. β0 is known as the coefficient of intercept and β1 is known as the coefficient of salary. β0 and β1 are the estimator of β0 and β1, β0 and β1 are sample statistics. Equation for line of best fit: Y=1.0388X-1908.797, where Y is the salary of manager(‘000dollars) and X  is the amount of sales(‘000 dollars).

(ii) The value of the intercept of the equation is -1908.797, it is the expected value of Y when X=0. In this case, the intercept would be the expected price of a zero-size of sales: -$1,908,797 and it is equal to $0 as it is impossible to have negative dollar. In these data, the range of X is from 1136-9873($’000). Since X=0 is well outside of this range, it is not meaningful to interpret the corresponding Y value.

(iii) The value slope of this equation is 1.039. For every $1000 of sales, expect salary of manager to rise by $1039.

(c)

(i) The value of the coefficient of determination is 92.28%.

(ii) Coefficient of determination(R square) measures how well the estimated regression equation fits the observed data. R square lies between 0-100%, if R square=0, there is no relationship between Y and X. If R square=1, it is an exact linear relationship. 92.28% of the variation in salary can be attributed to differences in amount of sales, and the remaining 7.72% of salary variability is unexplained.