The equation y = 2x + 1, coupled with the correlation coefficient r = 0.9908114438, strongly indicates a positive linear relationship between x and y. Here option A is correct.
The equation for the line of best fit, given by y = 2x + 1, implies that for every unit increase in x, y increases by 2 units, and the line passes through the point (0,1). This linear relationship is characterized by a positive slope, indicating a positive correlation between the variables x and y.
The correlation coefficient, denoted by r, quantifies the strength and direction of this linear relationship. In this case, r = 0.9908114438, which is very close to 1.
The correlation coefficient ranges from -1 to 1, where 1 signifies a perfect positive linear relationship. Since r is close to 1, it indicates a strong positive correlation between x and y. This means that as x increases, y also tends to increase, and vice versa.
The equation of the line of best fit and the high correlation coefficient provide strong evidence of a positive linear relationship between the variables, supporting the conclusion that the answer is (A).
Complete question:
The calculator screen shows a linear regression. Write the equation for the line of best fit for the data. Round values to the nearest integer. LinReg y = 2x+1 a = -1.96341463 b=19.09756098 c = 9817073171 d = -,9908114438
A. a strong positive correlation
B. a weak positive correlation
C. a strong negative correlation
D. a weak negative correlation