Problem: Write an article based on this summary: Set up your correlation coefficient equation. Solve for the correlation coefficient. Calculate R-squared.

Answer: The Pearson correlation coefficient is luckily a good amount simpler to calculate than its constituent parts, the covariance and standard deviations. The correlation coefficient of X and Y, xy{\displaystyle
ho _{xy}}, is calculated as xyxy{\displaystyle {
rac {\sigma _{xy}}{\sigma {x} imes \sigma {y}}}}. In simple terms, it is the covariance of X and Y divided by the product of their standard deviations. For the example stocks, your equation would be set up as xy=0.19250.4560.522{\displaystyle
ho _{xy}={
rac {0.1925}{0.456 imes 0.522}}} Start by simplifying the bottom of the equation by multiplying the two standard deviations. Then, divide the covariance on the top by your result. The solution is your correlation coefficient. The coefficient is represented as a decimal between -1 and 1, rather than as a percentage. Continuing with the example, the equation solves to xy=0.809{\displaystyle
ho _{xy}=0.809}. So, the correlation coefficient between returns on stocks X and Y is 0.809. Note that this result has been rounded to three decimal places. The square of the correlation coefficient, called R-squared, is also used to measure how closely the returns are linearly related. In simpler terms, it represents how much of the movement in one variable is caused by the other. It does, however, specify which variable acts upon the other (if X causes Y to move or if Y causes X to). Calculate R-squared by squaring your result for the correlation coefficient. For example, the R-squared value for the example correlation coefficient would be xy2=0.8092=0.654.{\displaystyle
ho _{xy}^{2}=0.809^{2}=0.654.}

Problem: Write an article based on this summary: Turn one cake onto a platter. Use a long serrated knife to trim off the rounded top of the cake. Finished.

Answer: Since the cake will be unwieldy once it is layered and iced, it's best to use the same plate on which you plan to serve the cake. Hold the knife parallel to the brim of the cake and slice about 14 inch (0.6cm) off the top. Be careful to slice straight across, holding the knife level as you go. Try to create a flat, even surface. This will serve as a base for the second layer. Remove the rounded top of the cake and discard it, or save it to eat. Don't attempt to cut off the top of the cake with a small knife, as this will result in an uneven surface.

Problem: Write an article based on this summary: Heat the oil in the pan. Add your onions to the oil. Reduce the flame to medium. Take out the onions from the pan.

Answer: Start with the stove heat on high to get the oil nice and hot, quickly. The onions should sizzle when you put them in the pan with the oil. Once you see oil evaporating a little bit, the oil is ready for the onions. It's easier to fry onions in smaller portions, so for 2 sliced onions, you can try frying 3 batches or so. Deep fry the onions on medium heat until they turn a golden brown. This should take about 10-20 minutes. While they are sizzling in the oil, gently mix the onions around to keep all of them coated, and to disperse the heat and oil evenly. If the flame is very high the onions will burn on the outside and remain watery on the inside. Use a big, perforated spoon (a spoon with holes in it for drainage) to removes the onions from the pan once they are golden brown. You want a perforated spoon to drain out excess oil. Place the onions on a plate with a paper towel on it, to absorb the rest of the excess oil. Put the onions aside for later.

Problem: Write an article based on this summary: Pick a recipe or create your own. Gather ingredients. Make the mask. Apply the mask. Apply toner and moisturizer to your skin.

Answer:
There are a variety of turmeric mask recipes that can be used on your face. These combine turmeric with ingredients that will both help your skin and help the turmeric stick to your skin. Common ingredients for a turmeric face mask include: honey, yogurt, milk, avocado, oat or chickpea flour, and lemon. One recipe you can use is to combine 2 tablespoons (30 ml) of chickpea flour, a quarter teaspoon (1 ml) of turmeric powder, 2 teaspoons (30 ml) of honey, and enough yogurt, milk, or water to make the mixture into a paste. For a really simple mask, simply combine a quarter teaspoon (1 ml) turmeric with 2 tablespoons (30 ml) of honey. This mixture is easily applied to the face due to the stickiness of the honey. For skin that is dry but also prone to breakouts, combine 1 tablespoon (15 ml) of turmeric with half a mashed avocado. Make your own special combination if you like! If you have any of the ingredients normally used in face masks on hand, simply combine what you have and use it. You can find dried turmeric in most natural food stores in the dietary supplement section. You can also easily find it and buy it online. If you are interested in using fresh turmeric, look in your local natural food store. Fresh turmeric is usually stored near fresh ginger in your store's produce section. It is not always available, so if you can't find it be sure to ask the produce worker at your store if it is available. Combine the ingredients of your mask in a bowl, making sure to mix ingredients completely. Whatever recipe you choose, make sure that the resulting mixture is liquid enough to apply to the face but not so runny that it will run off your face. This means that it should be the consistency of a thick mud. Apply the turmeric mask so it comes in direct contact with your acne. Use your fingers, a fan brush, or a small spatula to smooth the mixture all over your face. Apply a thick layer to your face so that the mask doesn't dry out too quickly. Like with all beauty masks, be sure to avoid getting it in your eyes, nose, or mouth, as this would be uncomfortable. Turmeric can stain your face yellow. You can remove any residual yellowness by lightly scrubbing your skin with a paste made of chickpea flour. Face masks and cleansers can upset your skin's natural pH balance and leave it either greasy or dehydrated. After washing off the mask, put on a little toner and follow it with your favorite moisturizer to rebalance the skin and lock in moisture.