Problem
Is there a relation between the age difference between husband/wives and the percent of a country that is literate? Researchers found the least-square regression between age difference (husband age minus wife age), $y$, and literacy rate (percent of the population that is literate), $x$, is $\hat{y}=-0.0501 x+6.8$. The model applied for $22 \leq x \leq 100$. Complete parts (a) through (e) below. For every unit increase in literacy rate, the age difference falls by 0.0501 units, on average. (Type an integer or decimal. Do not round.) (b) Does it make sense to interpret the $y$-intercept? Explain. Choose the correct answer below. A. Yes -it makes sense to interpret the $y$-intercept because an $\mathrm{x}$-value of 0 is within the realm of possibilities. B. No-it does not make sense to interpret the $y$-intercept because a y-value of 0 is impossible. c. No-it does not make sense to interpret the $y$-intercept because a $y$-value of 0 is outside the scope of the model. D. No-it does not make sense to interpret the $y$-intercept because an $x$-value of 0 is outside the scope of the model. E. No-it does not make sense to interpret the $y$-intercept because an $\mathrm{x}$-value of 0 is impossible.
Solution
Step 1 ：The problem is asking whether it makes sense to interpret the y-intercept in the context of the problem. The y-intercept is the value of y when x is 0. In this case, x represents the literacy rate and y represents the age difference between husband and wife.
Step 2 ：The y-intercept would represent the age difference when the literacy rate is 0. However, the model is only applicable for literacy rates between 22 and 100. Therefore, a literacy rate of 0 is outside the scope of the model.
Step 3 ：So, it does not make sense to interpret the y-intercept in this context.
Step 4 ：\(\boxed{\text{D. No-it does not make sense to interpret the y-intercept because an x-value of 0 is outside the scope of the model.}}\)
