Passage
and when she was baptized, and her household, she did call upon us, saying, `If ye have judged me to be faithful to the Lord, having entered into my house, remain;' and she constrained us.
and when she was baptized, and her household, she did call upon us, saying, `If ye have judged me to be faithful to the Lord, having entered into my house, remain;' and she constrained us.
Acts 16:13 on the sabbath-day also we went forth outside of the city, by a river, where there used to be prayer, and having sat down, we were speaking to the women who came together,
Acts 16:14 and a certain woman, by name Lydia, a seller of purple, of the city of Thyatira, worshipping God, was hearing, whose heart the Lord did open to attend to the things spoken by Paul;
Acts 16:15 and when she was baptized, and her household, she did call upon us, saying, `If ye have judged me to be faithful to the Lord, having entered into my house, remain;' and she constrained us.
Acts 16:16 And it came to pass in our going on to prayer, a certain maid, having a spirit of Python, did meet us, who brought much employment to her masters by soothsaying,
Acts 16:17 she having followed Paul and us, was crying, saying, `These men are servants of the Most High God, who declare to us a way of salvation;'
The verse centers on "faith", "baptized", "household", "call", "upon", "saying", "judged", and "faithful". It is saying that the verse draws attention to "faith" and "baptized", so its meaning should be read from those terms before moving to application.
The nearby context moves from verse 14's "and a certain woman by name Lydia..." into verse 16's "And it came to pass in our...", so "faith" and "baptized" belong inside that flow. In Acts context, the local focus is Christ, faith, and discipleship.
A plain takeaway is to answer the verse's own emphasis on "faith" and "baptized" with trust shaped by these words, not by a vague optimism outside the passage.