The stock market Some people think that the behavior of the stock market in January predicts its behavior for the rest of the year. Take the explanatory variable $x$ to be the percent change in a stock market index in January and the response variable $y$ to be the change in the index for the entire year. We expect a positive correlation between $x$ and $y$ because the change during January contributes to the full year's change. Calculation from data for an 18 -year period gives $$ \begin{array}{c}{\overline{x}=1.75 \% \quad s_{x}=5.36 \% \quad \overline{y}=9.07 \%} \\ {s_{y}=15.35 \% \quad r=0.596}\end{array} $$ (a) Find the equation of the least-squares line for predicting full-year change from January change. Show your work. (b) The mean change in January is $\overline{x}=1.75 \%$ . Use your regression line to predict the change in the index in a year in which the index rises 1.75$\%$ in January. Why could you have given this result (up to roundoff error) without doing the calculation?
Added by Adri-N M.
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Given: $r = 0.596$ $s_y = 15.35\%$ $s_x = 5.36\%$ Plugging in the values: $b = 0.596 \times \frac{15.35}{5.36} = 1.707$ ** Show more…
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The stock market Some people think that the behavior of the stock market in January predicts its behavior for the rest of the year. Take the explanatory variable $x$ to be the percent change in a stock market index in January and the response variable $y$ to be the change in the index for the entire year. We expect a positive correlation between $x$ and $y$ because the change during January contributes to the full year's change. Calculation from data for an 18 -year period gives $$\begin{array}{c}\bar{x}=1.75 \% \quad s_{x}=5.36 \% \quad \bar{y}=9.07 \% \\ s_{y}=15.35 \% \quad r=0.596\end{array}$$ (a) Find the equation of the least-squares line for predicting full-year change from January change. Show your work. (b) Suppose that the percent change in a particular January was 2 standard deviations above average. Predict the percent change for the entire year, without using the least-squares line. Show your work.
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Some people think that the behavior of the stock market in January predicts its behavior for the rest of the year. Let the explanatory variable be the percent change in a stock market index in January. Let the response variable be the percent change in the stock market index for the entire year. You have a data set with 50 cases (where each case is a calendar year). Based on this data, you have the following statistics: • mean of the x-variable: 2.04% • standard devation of the x-variable: 6.83% • mean of the y-variable: 9.98% • standard devation of the y-variable: 17.84% • correlation between the two variables: 0.68 What percent of the observed variation in yearly changes in the index is explained by a straight-line relationship with the change during January? Enter your answer in percent to 1 decimal place. Do not type the % symbol. Caution: do not enter the decimal proportion; enter your answer as percent. For example, a proportion of 0.571 is the same as 57.1%.
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The return on u stock is the change in its market price plus any dividend payments made. Total return is usually expressed as a percent of the beginning price. The figure Below shows a histogram of the distribution of the monthly returns for all common stocks listed on U.S. markets from January 1985 to September 20071273 months). $^{\text {25 }}$ The extreme low outlier represents the market crush of October $1987,$ when stocks last $23 \%$ of their value in one month. CAN'T COPY THE FIGURE (a) Ignoring the outliers, describe the overall shape of the distribution of monthly returns. (b) What is the approximate center of this distribution? In 1 Approximately what were the smallest and largest monthly returns, leaving out the outliers? (d) A return less than zero means that stacks lost value in that month. About what percent of all months had returns less than zero?
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