We use the form ý = a + bx for the least-squares line. In some computer printouts, the least-squares equation is not given directly. Instead, the value of the constant a is given, and the coefficient b of the explanatory or predictor variable is displayed. Sometimes a is referred to as the constant, and sometimes as the intercept. Data from a report showed the following relationship between elevation (in thousands of feet) and average number of frost-free days per year in a state. A Minitab printout provides the following information. Predictor Coef SE Coef т Conatant 317.97 28.31 11.24 0.002 Elevation -31.974 3.511 -8.79 0.003 S - 11.8603 R-Sq - 95.0e Notice that "Elevation" is listed under "Predictor." This means that elevation is the explanatory variable x. Its coefficient is the slope b. "Constant" refers to a in the equation ý = a + bx. (a) Use the printout to write the least-squares equation. ý = 317.97 (b) For each 1000-foot increase in elevation, how many fewer frost-free days are predicted? (Round your answer to three decimal places.) 31.974 (c) The printout gives the value of the coefficient of determination 2. What is the value of r? Be sure to give the correct sign for r based on the sign of b. (Round your answer to four decimal places.) (d) What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained?

Yummy Lunch Restaurant needs to decide the most profitable location for their business expansion. Marketing manager plans to use a multiple regression model to achieve their target. His model considers yearly revenue as the dependent variable. He found that number of people within 2KM (People), Mean household income(income), no of competitors and price as explanatory variables of company yearly revenue. The following is the descriptive statistics and regression output from Excel.       Revenue People Income Competitors Price             Mean 343965.68 5970.26 41522.96 2.8 5.68 Standard Error 5307.89863 139.0845281 582.1376385 0.142857 0.051030203 Median 345166.5 6032 41339.5 3 5.75 Mode #N/A 5917 #N/A 3 6 Standard Deviation 37532.51115 983.47613 4116.334718 1.010153 0.360838027 Sample Variance 1408689393 967225.2984 16944211.51 1.020408 0.130204082 Sum 17198284 298513 2076148…

Range of ankle motion is a contributing factor to falls among the elderly. Suppose a team of researchers is studying how compression hosiery, typical shoes, and medical shoes affect range of ankle motion. In particular, note the variables Barefoot and Footwear2. Barefoot represents a subject's range of ankle motion (in degrees) while barefoot, and Footwear2 represents their range of ankle motion (in degrees) while wearing medical shoes. Use this data and your preferred software to calculate the equation of the least-squares linear regression line to predict a subject's range of ankle motion while wearing medical shoes, ?̂ , based on their range of ankle motion while barefoot, ? . Round your coefficients to two decimal places of precision. ?̂  = A physical therapist determines that her patient Jan has a range of ankle motion of 7.26°7.26° while barefoot. Predict Jan's range of ankle motion while wearing medical shoes, ?̂ . Round your answer to two decimal places. ?̂ = Suppose Jan's…

A researcher want to know if there is a relationship between sleep and anxiety.  The researcher randomly selected n = 5 participants and asked each to rate their sleep quality and anxiety level on a scale of 1 to 5.  The data are below: Sleep X  Anxiety Y 2 2 3 3 2 2 4 2 5 2 Calculate the Sum of Squares for X (SSX)

Below is the output from regression.  Use the p-value and decide if the equation is good to use for forecasting.    Group of answer choices A.) p-value = 82 - equation is good to use B.) p-value = 0.15 - equation is not good to use C.) p-value = 0.18 - equation is not good to use D.) p-value = -16 - equation is good to use