Homework 4

• Slope is defined as change in value of Y while unit change in X.
• The slope can be calculated using the formula m = (y2 - y1) / (x2 - x1).
• The equation of a line with intercept on the vertical axis is given by y = mx + b.
• A straight line graph shows that there is a direct relationship between two variables, where an increase or decrease in one variable results in a corresponding change in another variable.
• A line with zero slope is called horizontal.
• A line that passes through the origin has an undefined slope, which means it cannot be determined.
• If two points are on the same vertical line, their slopes are not defined.
• A straight line graph is used to show the relationship between two variables, where one variable is plotted against another.
• In a scatter plot, data points are represented by dots or circles at their respective coordinates.
• The best-fitting Regression line can be used to predict the value of the dependent variable for a given value of the independent variable.
• M=sl',ope, b==intercept, x=independent variable, y=dependent variable
• The coefficient of Determination measures the proportion of the variation in the response//dependent variable that is explained by the explanatory/independent variable.
• The correlation coefficient r measures the strength and direction of linear association between two quantitative variables.
• When all values of an .independent Variable X are equal, it means that no variability in the dependent variable Y exists. in such cases, the regression model cannot capture any relationship between X and Y.
• The slope of the Lin represents the change in Y per unit change in X. Y=A+BX. A is the y-intercept. B is the slope.
• Simple linear regression is as statistical m method u used t to model the relationships between two variables where one variable is a response variable and the other is a predictor variable. The linear relationships between the two variables are represented by a line.
• The least squares method is used to estimate the parameters of a linear regression model.. It minimizes the sum of squares for error, which is the sum of the squared differences between predicted values and actual values
• R-square = SSR/SST * 100. SSR is sum of square due to regression. SST is sum of square total.
• SSE Standard Error of estimate formula is to divide S of the population by three square root of the number of elements