F ILE A researcher examines the factors that influence student performance. She gathers data on 224 school districts in Massachusetts. The response variable is the students'm ean score on a standardized test (Score). She uses four explanatory variables in her analysis: the studentto-teacher ratio (STR), the average teacher's salary (TSAL), the m edian household income (INC), and the percentage o f single fam ily households (SGL). A portion o f the data is shown in the accompanying table; the complete data set can be found on the text website, labeled MCAS.

Score STR (%)

TSAL

(in $1,000s)

INC

(in $1,000s) SGL (%)

227.00 19.00 44.01 48.89 4.70 230.67 17.90 40.17 43.91 4.60 230.67 19.20 44.79 47.64 5.10 SOURCE: M a s s a c h u s e tts D e p a r tm e n t o f E d u c a tio n a n d th e C e n s u s o f P o p u la tio n a n d H o u s in g .

a. Estimate Score = β 0 + β1 STR + β 2TSAL + β 3INC +

β 4SGL + ε and show th e regression results in a wellform atted table.

b. Suppose you w ant to test if school in p u t factors, STR and TSAL, are significant in explaining Score. Specify the com peting hypotheses. Estimate the restricted model. At the 5% significance level, can you conclude th a t STR and TSAL are jo in tly significant?

c. Suppose you w ant to test if socioeconom ic factors, INC and SGL, are significant in explaining Score. Specify the com peting hypotheses. Estimate the restricted model. At the 5% significance level, can you conclude th a t INC and SGL are jo in tly significant?