Would it make sense to use this model to predict the age difference between husband/wife in a country where the literacy rate is 8%?

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Question:

Is there a relation between the age difference between husband/wives and the percent of a country that is literate. Researchers found the least -squares regression between age difference (husband age minus wife age),y, and literacy rate (percent of the population that is literate), x, is y^=−0.0527x+7.1. The model applied for 18≤x≤100. (a) Interpret the slope. (b) Does it make sense to interpret they-intercept? Explain. (c) Predict the age difference between husband/wife in a country where the literacy rate is 25 percent. (d) Would it make sense to use this model to predict the age difference between husband/wife in a country where the literacy rate is 10 percent? Explain. (e) The literacy rate in the United States is 99 percent and the age difference between husbands and wives is 2 years. Is this age difference above or below the average age difference among all countries whose literacy rate is 99 percent?

Step-by-step explanation:

Given the model

          : y^ = − 0 . 0527x + 7.1

(a) The slope represents the average increase (decrease) in y per unit of x.

The age difference between husband and wife decreases by 0.0527 years per percentage (%) of literacy rate.

(b) It does not make sense to interpret the y intercept, because the literacy rate of 0 % is not in the given range of literacy rates ( 18 ≤ x ≤ 100 ) and the pattern between the variables could change outside of the given range of x - axis.

(c) Replace x in the given equation by 25 and evaluate:

we then have: y^ = − 0 . 0527 (25)  + 7.1 = 5.7825

Thus, the predicted age difference is 5.7825 years.

(d) It does not make sense to make a prediction for 10% literacy rate because the literacy rate of 10% is not in the given range of literacy rates

( 18 ≤ x ≤ 100 ) and the pattern between the variables could change outside of the given range of x - values

(e) Replace x in the given equation by 99 and we calculate thus

y^ = − 0 . 0527 (99)  + 7.1 = 1.8827

Hence, the average age difference is 1.8827 years and 2 years is then above the average age difference.

So the answers are :

(a) The average difference between husband and wife decrease by 0.0527 years per % of literacy rate

(b) No

(c) 5.7825 years

(d) No

(e) Above