For one thing, in To Kill a Mockingbird, Scout talks about Jem constantly. This book is about Scout growing up and she frequently compares changes in her own life to Jem's progression. She looks up to him and she's also empathetic and genuinely interested in what he's thinking. In Chapter 22, just after the guilty verdict, Scout narrates, “I stole a glance at Jem, but he was not listening. He would look up at Atticus, then down at the floor, and I wondered if he thought Atticus somehow responsible for Tom Robinson's conviction” (113). Scout often learned from the way Jem interacted with Atticus and other adults.
In Chapter 4, Scout narrates, “Jem was a born hero” (21). She is referring to his courage in portraying Boo Radley and keeping their game secret from Atticus. This is the most direct statement of Scout's admiration of her brother. Later, Jem would show much more courage in defending Scout from Mr. Ewell.
There are plenty of examples that are less direct. When Jem got to the second grade (Chapter 7) she noted that the only good thing was that she got to walk home with Jem. Overall, the evidence that Scout looks up to Jem is shown by how often she wonders what he's thinking. In fact, when she senses Jem is in a mood, she'll avoid him until the mood has passed. She does not agree with everything Jem does or says but she constantly cross references her feelings and thoughts with her guesses of what Jem is thinking. This preoccupation with Jem might be the initial model of how Scout learns to see things from the perspective of others. It was Atticus who taught her to put herself in other people's shoes.