Question

10) Which of the following statements are right?i. The first step in simple regression analysis usually is to construct a scatter plot.

ii. In simple regression analysis, the error terms are assumed to be linear, independent, and normally distributed with zero mean and constant variance.
iii. The proportion of variability of the dependent variable (y) accounted for or explained by the independent variable (x) is called the coefficient of correlation.

Answer 1

The first step in simple regression analysis is to construct a scatter plot. The error terms in simple regression analysis are assumed to be linear, independent, and normally distributed. The proportion of variability accounted for or explained by the independent variable is called the coefficient of correlation.

Step-by-step explanation:

a. The independent variable is x, and the dependent variable is y.

b. To draw a scatter plot, plot the x-values on the horizontal axis and the corresponding y-values on the vertical axis.

c. To find the line of best fit and the correlation coefficient, we use regression analysis. Regression analysis calculates the equation of the line that best represents the relationship between the independent and dependent variables. It also calculates the correlation coefficient, which measures the strength and direction of the linear relationship.

d. The correlation coefficient measures the strength and direction of the linear relationship between the independent and dependent variables. It ranges from -1 to 1, where -1 indicates a strong negative correlation, 1 indicates a strong positive correlation, and 0 indicates no correlation.

e. Yes, if the scatter plot shows a roughly straight line, then there is a linear relationship between the variables. If the scatter plot does not show a straight line, then there is no linear relationship between the variables.