Final answer:
The equation r-1.97=0.65 is an algebraic equation solved by adding 1.97 to both sides, giving r=2.62. In statistics, 'r' represents the correlation coefficient, and if it is greater than the critical value, it is significant for predictions. Correlation coefficients are used in various statistics analyses, including regression analysis for prediction, such as estimating the Consumer Price Index (CPI).
Step-by-step explanation:
The student's question r-1.97=0.65 appears to be a mathematical equation and is related to algebra, a subfield of mathematics. To solve the equation for r, you would add 1.97 to both sides to isolate the variable:
r - 1.97 + 1.97 = 0.65 + 1.97
Therefore, r = 2.62.
In the context of statistics and correlation, significant r values and predicting relationships could imply that 'r' refers to the correlation coefficient. When the correlation coefficient 'r' is greater than the critical value from the table, it is considered significant and may be used for predictions. For instance, if r=0.8694 and the critical value for a given degree of freedom is ±0.532, since 0.8694 is greater than 0.532, the correlation is significant.
In a different context, say predicting inflation rates, a formula like ý-3204 + 1.662(Year) might be used to estimate changes in the Consumer Price Index (CPI) over time.