Final Answer:
The y-intercept of 37 represents the predicted score for zero hours studied. Using the regression line equation (y = mx + 37), substituting x = 5 yields a predicted score of 74, supporting the answer c). This indicates a positive relationship between study hours and test scores.Thus option c is te correct option.
Step-by-step explanation:
The y-intercept of the fitted line represents the predicted test score when the number of hours studied is zero. In this case, the y-intercept is given as 37. This means that if a student spent zero hours studying, their predicted test score would be 37. However, in practical terms, spending zero hours studying is not applicable, so we are interested in predicting the test score for a student who spent 5 hours studying.
The regression line provides the relationship between the number of hours studied (x) and the predicted test score (y). The equation of the line can be written as y = mx + b, where m is the slope and b is the y-intercept. In this case, the equation is y = mx + 37. To find the predicted test score for 5 hours of study, substitute x = 5 into the equation: y = m(5) + 37. The resulting value is the predicted test score for a student who spent 5 hours studying.
By calculating this, we find that y = 74, indicating that the predicted test score for a student who spent 5 hours studying is 74. Therefore, the correct answer is option c) 74. This suggests that, based on the regression analysis, spending more time studying positively influences the test score, and the predicted score for 5 hours of study is 74.
Thus option c is te correct option.