Final answer:
The correct answer is option 4. Omitting a variable that is correlated with both the dependent variable and an explanatory variable can lead to omitted variable bias. If length is omitted from a regression estimating the effect of weight on fuel efficiency, the coefficient on weight is expected to be more negative and have a larger standard error due to this bias.
Step-by-step explanation:
The question asks which of the following best describes what you would expect to find if you estimated the simple linear regression of mpghwy (highway miles per gallon) on weight, omitting length. The presence of a variable that is correlated with both the explanatory variable and the dependent variable, but is omitted from the regression, can potentially lead to omitted variable bias. In this case, if length is correlated with both weight and mpghwy and is not included in the regression, this might lead to an overestimation or underestimation of the association between weight and mpghwy.
Since length is likely positively correlated with weight and possibly negatively correlated with fuel efficiency, omitting length might lead the model to attribute the effect of length on fuel efficiency to weight. Therefore, the estimated coefficient on weight might be more negative than it truly is if length were included. Concerning the standard error, if an important variable like length is omitted, it generally leads to higher standard errors as the variability that length explains in fuel efficiency is incorrectly attributed to weight.
The correct option is: The estimated coefficient on weight would be more negative, and its standard error would be larger.