A student is predicted to earn a test score of 76. Which of the following values best represents the number of years that he or she has studied Spanish? Assume that there is a significant linear correlation between years of study and test score.
A) 4.1 years
B) 3.4 years
C) 2.9 years
D) 2.1 years
There is not enough information to determine which option is the best answer. A significant linear correlation between years of study and test score does not necessarily indicate a specific value for the number of years of study based on a predicted test score of 76. Other factors such as the slope and intercept of the linear regression equation would need to be known in order to make a more informed estimate.
A collection paired data consists of the number of years that students have studied Spanish and their scores on a Spanish language profiency test. A computer program was used to obtain the least squares linear regression line and the computer output is shown below. Along with the paired sample data the program was also given an x value of 2 years of study to be used for predicting test score.
Equation: y=mx+b
Statistics:
•r^2=0.83
•r=0.91
Parameters:
• m=10.90
• b=31.55
A student is predicted to earn a test score of 76. Which of the following values best represents the number of years that he or she has studied Spanish? Assume that there is a significant linear correlation between years of study and test score.
A) 4.1 years
B) 3.4 years
C) 2.9 years
D) 2.1 years
Using the given regression equation y = mx + b, where y represents the test score and x represents the number of years of study, we can solve for x with the given predicted score of 76:
76 = 10.90x + 31.55
44.45 = 10.90x
x ≈ 4.1 years
Therefore, the best choice for the number of years the student has studied Spanish is option A) 4.1 years.
In order to determine the best value that represents the number of years the student has studied Spanish, we need to analyze the given information.
Since there is a significant linear correlation between years of study and test score, we can assume that the score increases as the number of years studied increases.
Given that the student is predicted to earn a test score of 76, we can use this information to choose the best value for the number of years studied.
Looking at the options provided, the best value that represents the number of years studied would be the value that corresponds to a test score of 76.
From the options given, the closest value to a test score of 76 is option B) 3.4 years.
Thus, the best value that represents the number of years the student has studied Spanish is 3.4 years.