He nodded slowly, but I could tell there was still a bit of confusion roaming around in his mind. That was probably because the word slope hadn’t been mentioned yet.
“Then the slope, or as it’s written here, the impact, tells you how much the revenue increases for every extra dollar you spend on advertising.”
He didn’t move or say anything, so I turned the laptop back toward him and pointed at the figures.
“Look at the slope here. In this instance, it’s 3.1. So what do you think that means?”
He stared at the screen for a while, and I could tell that he wasn’t panicking. Instead, he was absorbing the information and actually thinking about it.
“I think it means… that for every dollar they spent on advertising they made three dollars and ten cents.”
He looked at me anxiously, and I could instantly tell that it was more of a question than an answer.
“Yes, that’s exactly what it means,” I said, giving him a reassuring smile.
His eyebrows shot up. “So the advertising isn’t just paying for itself. It’s bringing in a profit too.”
“According to this model, yes, but it’s important to remember that the outcome will get a different result every time you change the figures.”
He leaned back for a moment to process the information, but then he quickly shot up and pointed at another number.
“What does R-squared stand for?”
“That tells you how much of the change in revenue is explained by advertising.”
He scanned the screen. “Sixty-seven percent.”
I nodded. “So the advertising explains more of the variation in revenue, but not all of it. Even though advertising is a very important factor, other things still matter too.”
He was quiet for a good while. Then he turned to me as if a light bulb had gone off in his head.
“So this is just pattern recognition?”
I gave him a faint smile. “Yes.”
“Like reading coverage?”
“Exactly.”
The tension in his shoulders loosened, and suddenly he looked like a completely different man. He looked less like someone who was drowning under the pressure and more like someone who had just learned how to swim.
“Okay,” he said, sounding more confident. “I could get the hang of that one.”
“Good,” I said, feeling rather proud of myself. “So let’s move on to the profitability question then.”
His newfound confidence dissolved as he groaned. “That’s where I spiral.”
“You spiraled with the last one too until you could understand it,” I teased. “What makes you think this will be different?”
He gave me another one of those skeptical looks before motioning to the laptop. This was the kind of thing I had to explain even more carefully.
“According to the assignment, the company has a monthly revenue of forty-five thousand dollars. That’s the average, but like everything else, it has variations. Some months they earn more and other months they earn less.”
“Like a team’s average points per game,” he said with a nod.
“Exactly. The standard deviation tells you how spread out those numbers usually are.”
He squinted at the screen. “So it’s like… how chaotic a team is.”