1.
The method of least squares finds the best fit line that _____ the error between observed and estimated points on the line
Correct Answer
B. Minimize
Explanation
The method of least squares finds the best fit line that minimizes the error between observed and estimated points on the line. This means that it aims to reduce the overall difference between the observed data points and the estimated values on the line, making it the best possible fit. By minimizing the error, the method of least squares ensures that the line is as close as possible to the actual data points.
2.
The normal equation for fitting of a straight line y = a + bx is ∑ y =_____ _
Correct Answer
A. Na + b∑x
Explanation
The normal equation for fitting a straight line y = a + bx is given by na + bâˆ‘x. This equation represents the sum of the y-values (âˆ‘y) being equal to the product of the number of data points (n) and the y-intercept (a), plus the product of the slope (b) and the sum of the x-values (âˆ‘x).
3.
If the regression equation is equal to Y=23.6−54.2X, then 23.6 is the _____ while -54.2 is the ____ of the regression line
Correct Answer
C. Intercept,slope
Explanation
In a regression equation, the coefficient of the independent variable (X) is known as the slope, while the constant term (Y-intercept) is known as the intercept. In this case, the regression equation Y=23.6-54.2X indicates that 23.6 is the intercept and -54.2 is the slope of the regression line.
4.
In the model Y=mX+a, Y is also known as the:
Correct Answer
D. Predicted (dependent) variable
Explanation
In the given model Y=mX+a, Y is the predicted (dependent) variable. This means that the value of Y is dependent on the value of X, which is the independent variable. The equation represents a linear relationship between the independent variable X and the predicted variable Y, where m represents the slope of the line and a represents the y-intercept. The predicted variable Y is the variable that is being estimated or predicted based on the values of the independent variable X.
5.
The normal equations obtained after applying least square criteria in curve fitting can be solved by
Correct Answer(s)
A. Gauss Elimination method
C. Cramers rule
Explanation
The normal equations obtained after applying the least square criteria in curve fitting can be solved by Gauss Elimination method and Cramer's rule. The Gauss Elimination method is a systematic way of solving a system of linear equations by eliminating variables. Cramer's rule is a method that uses determinants to solve a system of linear equations. Both methods can be used to find the solutions to the normal equations and determine the coefficients of the curve fitting equation.
6.
WHAT TYPE OF MODEL SEEMS APPROPRAITE FOR EACH OF THE 3 ( IN order from left to Right1
Correct Answer
D. EXPONENTIAL,LINEAR,POWER
Explanation
The given answer suggests that an exponential model seems appropriate for the first set of data, a linear model seems appropriate for the second set of data, and a power model seems appropriate for the third set of data. This implies that the relationship between the variables in the first set can be described by an exponential function, the relationship in the second set can be described by a linear function, and the relationship in the third set can be described by a power function.
7.
The normal equation for fitting of a straight line y = ax + b is ∑xy =_____ _
Correct Answer
B. =a∑x^2 +b∑x
Explanation
The given equation is the result of applying the normal equation for fitting a straight line to the data. The equation is in the form of ∑xy = a∑x^2 + b∑x, where ∑xy represents the sum of the products of x and y values, ∑x represents the sum of all x values, ∑x^2 represents the sum of the squares of x values, a is the slope of the line, and b is the y-intercept of the line. Therefore, the correct answer is =a∑x^2 + b∑x.
8.
A process by which we estimate the value of dependent variable on the basis of one or more independent variables is called:
Correct Answer
C. Regression
Explanation
Regression is the correct answer because it refers to the process of estimating the value of a dependent variable based on one or more independent variables. In regression analysis, a mathematical equation is used to model the relationship between the dependent variable and the independent variables, allowing for predictions to be made about the dependent variable based on the values of the independent variables.
9.
The value of coefficient of correlation lies between
Correct Answer
A. -1 to 1
Explanation
The coefficient of correlation measures the strength and direction of the linear relationship between two variables. It can range from -1 to 1, where -1 indicates a perfect negative correlation, 0 indicates no correlation, and 1 indicates a perfect positive correlation. Therefore, the correct answer is -1 to 1.