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=−0.0437x+7.5. The model applied for 17≤x≤100. Interpret the slope. Select the correct choice below and fill in the answer box to complete your choice. For every unit increase in ____ the _ falls by ____ units, on average.

For every unit increase in literacy rate (percent of the population that is literate) the age difference (husband minus wife age) falls by 0.0437 units, on average.

Step-by-step explanation:

For this case we have that the regression model adjusted between age difference (husband minus wife age) representing the y variable and literacy rate (percent of the population that is literate) representing the variable x is given by:

[tex] y= -0.0437 x + 7.5[/tex] where [tex] 17 \leq x\leq 100[/tex]

And we know that the method used in order to adjust the regression line was least squares.

For this case our dependent variable is y = age difference (husband minus wife age) and the independent variable is x=literacy rate (percent of the population that is literate)

If we compare the regression model adjusted with the linear regression model:

[tex] y = \beta_1 x + \beta_o[/tex]

With [tex]\beta_1 [/tex] representing the slope we have that:

[tex] \hat \beta_1 = -0.0437[/tex]

[tex]\hat \beta_o = 7.5[/tex]

And we are interest on this case the interpretation about the slope and we can conclude that:

For every unit increase in literacy rate (percent of the population that is literate) the age difference (husband minus wife age) falls by 0.0437 units, on average.