1. An experiment was run and the following data table was produced: Input Response 2.5 3 4 4.5 (a) Calculate the correlation coefficient for the data. Is the data positively or negatively correlated, and is that correlation weak, moderate, or strong? (b) Find the equation of the least squares regression line and plot the line on top of a scatterplot of the data.
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- Suppose a doctor measures the height, x, and head circumference, y, of 11 children and obtains the data below. The correlation coefficient is 0.904 and the least squares regression line is y=0.208x+11.736. Complete parts (a) and (b) below.Suppose a doctor measures the height, x, and head circumference, y, of 11 children and obtains the data below. The correlation coefficient is 0.899 and the least squares regression line is y=0.185x+12.276. Complete parts (a) and (b) below. Height, x 27.75 25.75 26.75 25.75 28 26.5 25.75 26.75 27 27.25 27.25 Head Circumference, y 17.4 17.1 17.2 16.9 17.4 17.1 17.1 17.3 17.3 17.3 17.4 (a) Compute the coefficient of determination, R2. R2=nothing% (Round to one decimal place as needed.) (b) Interpret the coefficient of determination. Approximately nothing% of the variation in ▼ height head circumference is explained by the least-squares regression model. (Round to one decimal place as needed.)From the below table, Use excels to find the answer for the below questions: State Percentage Proficient in Reading Percentage Proficient in Mathematics California 60 59 Texas 73 78 New York 75 70 Florida 66 68 Illinois 75 70 Pennsylvania 79 77 Ohio 79 76 Michigan 73 66 Georgia 67 64 North Carolina 71 73 Activities: Compute the least-squares regression line for predicting math proficiency from reading proficiency. Interpretation of the least-squares regression line in part a.
- A scatterplot of student height, in inches, versus corresponding arm span length, in inches, is shown below. One of the points in the graph is labeled A. If the point labeled A is removed, which of the following statements would be true? The slope of the least squares regression line is unchanged and the correlation coefficient increases. The slope of the least squares regression line is unchanged and the correlation coefficient decreases. The slope of the least squares regression line increases and the correlation coefficient increases. The slope of the least squares regression line increases and the correlation coefficient decreases. The slope of the least squares regression line decreases and the correlation coefficient increases.A regional distributor of NIKE shoes is in the process of analyzing the factors that influence thedemand for the NIKE brand. The distributor hired an economist to conduct a study on the demand for this product. The economist collected quarterly time series data from 1986Q1 to 1991Q4 on the following variables:SALES Sales of NIKE shoesRPDI Real personal disposal incomeCONF Consumer confidence indexD2 Dummy variable for quarter 2D3 Dummy variable for quarter 3D4 Dummy variable for quarter 4Ordinary Least Squares was applied using sales as the dependent variable and real personal disposal income, consumer confidence index, dummy variable for quarter 2, dummy variable for quarter 3, and dummy variable for quarter 4 as independent variables. The table below shows the OLS output.Model 1: OLS, using observations 1986:1-1991:4 (T = 24)Dependent variable: SALESCoefficient Std. Error t-ratio p-valueconst −139.452 61.8421 −2.255 0.0368 **RPDI 1.56286 0.438492 3.564 0.0022 ***CONF 0.256247…A regional distributor of NIKE shoes is in the process of analyzing the factors that influence thedemand for the NIKE brand. The distributor hired an economist to conduct a study on the demand for this product. The economist collected quarterly time series data from 1986Q1 to 1991Q4 on the following variables:SALES Sales of NIKE shoesRPDI Real personal disposal incomeCONF Consumer confidence indexD2 Dummy variable for quarter 2D3 Dummy variable for quarter 3D4 Dummy variable for quarter 4Ordinary Least Squares was applied using sales as the dependent variable and real personal disposal income, consumer confidence index, dummy variable for quarter 2, dummy variable for quarter 3, and dummy variable for quarter 4 as independent variables. The table below shows the OLS output.Model 1: OLS, using observations 1986:1-1991:4 (T = 24)Dependent variable: SALESCoefficient Std. Error t-ratio p-valueconst −139.452 61.8421 −2.255 0.0368 **RPDI 1.56286 0.438492 3.564 0.0022 ***CONF 0.256247…
- 1. An article included a summary of findings regarding the use of SAT I scores, SAT II scores, and high school grade point average (GPA) to predict first-year college GPA. The article states that "among these, SAT II scores are the best predictor, explaining 17 percent of the variance in first-year college grades. GPA was second at 15.3 percent, and SAT I was last at 13.6 percent." If the data from this study were used to fit a least squares line with y = first-year college GPA and x = high school GPA, what would the value of r2 have been? r2 =_______ 2. A study was carried out to investigate the relationship between the hardness of molded plastic (y, in Brinell units) and the amount of time elapsed since the plastic was molded (x, in hours). Summary quantities include n = 15, SSResid = 1,237.628, and SSTo = 24,619.737. Calculate and interpret the coefficient of determination. (Round the coefficient of determination to four decimal places when written as a decimal and 2 decimal…In order to determine a realistic price for a new product that a company wants to market the company’s research department selected 10 sites thought to have essentially identical sales potential and offered the product in each at a different price. The resulting sales are recorded in the accompanying table: Price ($) Sales ($1,000s) 15.00 15 15.50 14 16.00 16 16.50 9 17.00 12 17.50 10 18.00 8 18.50 9 19.00 6 19.50 5 c). Find the equation of the sample regression line using Minitab. d). Interpret the meaning of the coefficients of the equation of the sample regression line.The following table presents the percentage of students who tested proficient in reading and the percentage who tested proficient in math for each of the ten most populous states in the United States. State Percent Proficient in Reading Percent Proficient in Mathematics California 60 59 Texas 73 78 New York 75 70 Florida 66 68 Illinois 75 70 Pennsylvania 79 77 Ohio 79 76 Michigan 73 66 Georgia 67 64 North Carolina 71 73 Compute the least-squares regression line for predicting math proficiency from reading proficiency. Predict the math proficiency for another state with reading proficiency of 63 percent.
- Computer output from a least-squares regression analysis based on a sample of size 17 is shown in the table. Term COEFCOEF SE CoefSE Coef TT Constant 7.43 0.59 12.59 xx 5.65 1.14 6.45 Assuming all conditions for inference are met, which of the following defines a 95 percent confidence interval for the slope of the least-squares regression line?consider the coefficient estimates of the following market model linear regression of general motors (gm) on the S&P500 market returns coefficient estimate std error tvalue pr(>ItI) intercept 0.005860 0.0003704 1.582 0.12412 sp500 0.0904753 0.266702 3.392 0.00196 The number of observations is 32.At the 1% significance level, what is the (1)test statistic value,(2) the critical values (3) decision regarding the null hypothesis that the beta coefficient on the market returns is equal to 1.61The director of marketing at Vanguard Corporation believes that sales of the company's Bright Side laundry detergent (S) are related to Vanguard's own advertising expenditures (A), as well as the combined advertising expenditures of its three biggest rival detergents (R).The marketing director collects 36 weekly observations on S, A, and R . Vanguard's marketing director is comfortable using parameter estimates that are statistically significant at the 10 percent level or better. Give the specific statistical tool that can be used to this problem.