12 - Elizabeth
Elizabeth
I stepped into the library and took a deep breath. It was one of my favorite places on the planet. I loved the smell of the books and the quiet that the place offered. It was something I had found nowhere else.
My eyes scanned over the seats that were filled with students as I looked for a place of my own, but something else caught my eye.
Ethan was sitting in a dark corner, and he looked like he was losing a game that no one knew he was playing.
There were books and papers scattered across the table, and he was furiously typing on his dimly lit laptop.
His hair was messy. His coffee was probably ice-cold, and his mismatched clothes told me he hadn’t slept in days. There was something serious on his mind, and I had to find out what it was before it consumed him even more than it already had.
I approached slowly and got an even better idea of what was coming to me.
His notebook had thick, aggressive cross-outs, and he was slamming his finger against the calculator as if it offended him.
He was so preoccupied that he didn’t even notice I was coming until I pulled the chair opposite him out.
“Before you even think of saying anything,” he said without looking up. “Just know that I absolutely hate this class.”
I leaned over to read the header on his screen. Business statistics: Regression and probability analysis.
“That’s dramatic,” I said with a concerned look. “But I don’t think you hate it. I just think you might not understand it.”
“Are you calling me stupid?”
“No,” I rolled my eyes. “But the art of learning is all in the way things are explained to a student. Some teachers master that craft. Others don’t. Obviously, yours is the latter.”
He finally looked up, and the face staring at me didn’t belong to the guy I knew. There wasn’t any gameplay in his eyes. There was no swagger, only frustration. “That’s even worse.”
I studied him for a minute longer than I meant to and realized that there was something else hidden in his gaze. It was much darker and so much heavier.
“I can’t fail this,” he muttered. “This stupid project is worth 50% of my grade. And I’ve already wasted three weeks on it. Which has gotten me absolutely nowhere, just by the way.”
“I thought jocks were supposed to be all about the short,” I joked, hoping it would lighten the mood.
“If only it were that simple,” he said, resting his face in his hands. “I’m not officially on a scholarship here, because Stamford couldn’t transfer it. So my stay is conditional. If my GPA drops, so does my funding.”
That’s what it was. He wasn’t being arrogant or proud. He was under a mountain of pressure that none of us could see. We all thought his ego was ruling him because no one would ever expect a man like him to be drowning under the pressure.
There was so much that I could say to lighten the mood, but I chose not to. He didn’t need to feel like I wasn’t taking his situation seriously. He needed help, and I wanted to give it to him.
“Okay,” I said as I grabbed his notebook. “Show me where it stopped making sense.”
“It never made sense to begin with,” he scoffed, but he turned his laptop toward me and tapped the screen. “Correlation, Regression and Intercepting the slope. They all blend and eventually I’m looking at a bunch of figures that make absolutely no sense at all.”
I scanned over his assignment and realized that it wasn’t as bad as he was making it out to be. In fact, it could be super easy if he just looked at it the right way.
“So… a sports equipment company is analyzing whether increased advertising led to higher sales across its branches,” I said to no one in particular. There are multiple variables and a lot of revenue data. They also have a threshold that they want to hit consistently.”
“Yeah. If any of that makes sense to you,” he said.
“It makes complete sense,” I said, trying my absolute best not to sound condescending. “Your problem is that you’re looking at the entire thing the wrong way. You’re trying to memorize the steps. That’s why it becomes a number salad for you.”
He looked at me as if I had grown a second head. “How else do you expect me to do it?”
I looked at him and smiled. He was such a tough, unbreakable guy, but in so many aspects, he was just a little boy.
His way of thinking about this problem proved it.
On the field he could find so many different strategies on the fly, but for something he felt he couldn’t understand, he drew a total blank. It was quite adorable.
“With many things in life, the tried and tested strategy doesn’t work. In real-life situations, improvise to find a solution. But in order to do that, you need to understand the thing you’re working with. This is one of those cases.”
He leaned back skeptically. Like my methods were alien. “I don’t seem to understand where you’re coming from. So please enlighten me and explain this seemingly simple—yet apparently impossible—theory of yours.”
I moved to the chair next to him so it would be easier for us to work through these things.
“Always start simple. Correlation, for example, just measures whether or not two things move together.”
“I get that,” he said smugly, and I raised a brow.
“I don’t think you do. What you understand is the definition. It’s simple enough after all, but take a moment to really think about it.”
I gave him a moment to absorb the concept completely, but he seemed to have drawn a blank. I tilted my head slightly and admired the view.
“If a team practices more, do they usually win more?” I asked, hoping to nudge him in the right direction.
His mouth twitched despite the fact that he was trying to remain serious. “Are you really making this about football?”
“Of course I am. You should always try to look at things you’re struggling with from the perspective of something you like. It makes it a lot easier.”
He gasped in astonishment. “Okay, yes. More practice usually means more wins.”
I smiled at his reaction. I didn’t know if he was actually starting to understand it or not, but he was definitely trying, which was a lot more than I expected to get out of him.
“Usually,” I repeated, highlighting the word and its importance. “But not always. That ‘usually’ is the correlation. It tells you how strongly practice and wins move together.”
He looked back at his spreadsheet and tapped a highlighted section. “So in this case, advertising would be the practice?”
I smiled. “Yes, and the revenue would be the wins.”
“Can you show me?” Ethan asked sheepishly.
With a smile, I pulled his laptop closer and added the numbers to his spreadsheet. The correlation coefficient came back as a strong 0.82, and his posture shifted so quickly that he nearly fell off his chair.
“That’s good, right?” He asked cautiously.
“That’s very good,” I assured him. “It means that advertising and revenue move together strongly. When ad spend increases, revenue increases too.”
“If that’s the case, why doesn’t management just pour money into advertising?”
“Don’t jump the gun,” I said, nudging his notebook. “Correlation only tells us they’re related, but it doesn’t tell us how much the revenue increased.”
For a moment his shoulders sagged, but then he perked back up and leaned forward. It was as if he was more focused and ready to take on the world.
“That would be regression, right?” he asked.
I gave him a smile. “Now you’re getting the hang of it.”
He pointed at the output summary on the screen. “This is where I keep getting lost. The slope thingy. I don’t understand what it actually means.”
“Okay,” I said, grabbing his pencil and flipping to a clean page in his notebook. “Forget the technical terms. They’re like designed to confuse you.”
In large letters I wrote: Revenue = Base Sales + Impact of Advertising.
“Base sales,” I explained, tapping the word. “Is how much a company would make if it spent no money on advertising.”
“Okay, that makes sense because people would go to the store and still end up buying stuff.”
“Correct. That has to do with their location, brand loyalty, and the habits that people have.”
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.”
I bit my lip, trying not to laugh because I wasn’t sure if he was being serious or making a joke.
“Define chaotic.”
He thought about it for a good long moment. “Like when a team scores forty points one week and seventy the next.”
“That,” I said, pointing the pencil at him. “Is standard deviation.”
He nodded slowly. “So being consistent means you have a low standard deviation?”
“Yes.”
He leaned back in his chair and put his arms behind his head. For a moment I thought he’d lift his feet too, but luckily he didn’t go that far.
“So if a player throws three hundred yards one week and ninety the next…”
“They’re unstable.”
“Or exciting.”
“Definitely unstable.”
He smirked. “That would depend on who you ask.”
I rolled my eyes, but couldn’t stop the smile from spreading across my face. He was loosening up, which was more than I had hoped for when I got into this.
“In statistics, exciting usually means unreliable.”
“Wow,” he said dryly. “That feels like a personal attack.”
I ignored his comment because I thought maybe it was a good thing for him to believe that it was. Only for a little while, of course.
“Okay, the company’s average is forty-five thousand, and the standard deviation usually tells us how much above or below that the company swings on average.”
“Fifty thousand?” He asked.
“Is above average.”
“Obviously,” he said smugly.
I playfully slapped his chest because he was becoming far too cocky for his own good. If he kept messing around, he could end up missing something important.
“Thank you for that, Captain Insight. But the question is, how far above average?”
He studied it more carefully, as if it were a trick question. “Five thousand?”
“Right, so the standard deviation is five thousand.”
“So it’s one full standard deviation above the mean?”
I wanted to say no just to mess with him, but his eyes were as large as saucers, and that made it impossible for me to pull off my joke.
“Look at you, Mr. Smarty-pants.”
“I’m evolving,” he said.
“Don’t get ahead of yourself,” I teased.
Before I could say more, we heard a familiar voice. “There you are!” Jenna said.
Ethan just froze.
“Don’t tell me you forgot about the party,” Jenna told me. “We need to get ready.”
I hesitated because I was actually having a lot of fun with Ethan, and I didn’t want to cut it short. Plus, he had already learned so much. He was about to finish his project. And I wanted to help him get to that point, but then he started collecting all his stuff, and he looked so unaffected.
Something about the way he was acting made my chest clench up. It seemed so unfair to drop him in the middle of it all, especially since there would be plenty of other parties to attend.
“Before you go…” he said softly. “Would you mind officially tutoring me?”
I was floored, but he wasn’t joking or flirting. He was as serious as I had ever seen him.
“Like… on a regular basis,” he added. “I don’t want to lose this. You’re… great. Really great.”
My heart nearly exploded. He was being so understanding, and there was so much momentum, but it was those words and the way he said them that made me crumble.
“I’d love to,” I said, giving him a warm smile.
His eyes lifted to mine, and there was something unguarded in them.
“Are you serious?”
“Yeah.” I slipped my bag over my shoulder. “We’ll do it twice a week.”
“At a minimum,” he said, giving me one of his dazzling smiles.
I winked at him. “You don’t fix fundamentals overnight.”