Question

At issue is the relationship between the weight of an infant and the number of hours of sleep the infant gets per day. Attached is an Excel file with sample data for the weight (in pounds) and the number of hours of sleep. Mod4-WeightxHours-Regression-QuantQuiz.xlsx Run regression in Excel and respond to the following questions. Note: this is a small enough data set it's also good practice for the calculator. You can check your work and make sure you get the same answers in both places! a. The correlation coefficient between weight and hours - Enter your answer rounded to 2 decimals, in the format 0.12 or -0.12. b. What percent of the variation in hours of sleep is explained by the variation in the babies' weight? Enter your answer rounded to 2 decimals, in the format 0.12. c. The linear equation is y-hat = Enter both answers rounded to 2 decimals, in the format 1.23 or -1.23, with no other text or symbols. d. With 95% confidence, a one-pound increase in weight will change the predicted hours of sleep by hours. This question is asking for the confidence interval estimate for the regression slope coefficient. Enter the values from your Excel regression output, rounded to 2 decimals, in the format -1.23 or 1.23, with no other text or symbols.

Answer 1

We have to use excel and solve: here indepndent variable is Weight and dependent variable is Hours spent : DATA > Data Analysis > Regression > y input chose as Hours spent and x input as Weight SUMMARY OUTPUT Regression Statistics Multiple R 0.759908947 R Square 0.577461607 Adjusted R Squa 0.507038542 Standard Error 0.505952412 Observations ANOVA Significance F 0.028668269 1 Regression Residual Total MS F 2.099072942 2.099073 8.199893 1.535927058 0.255988 3.635

t Intercept Weight(x) Coefficients 15.9327119 -0.206805216 Standard Error 0.740519018 0.072219985 Stat P-value 21.5156 6.58E-07 -2.86355 0.028668 Lower 95% Upper 95% ower 95.0%pper 95.0% 14.12072714 17.74469666 14.12073 17.7447 -0.383521153 -0.030089279 -0.38352 -0.03009 ##a) correlation between weight and hours spent : 0.76 ##b) what percent of variation in hours of sleep explained by the variation in the babies weight 0.58 ##c) the linear equation y hat is 15.93 -0.20 * weight ##d) with a 95% confidence, a one pound increase in weight will change the predicted hours of sleep by -0.38 to -0.03 hours ##e) p value 0.029 ##f) at alpha = 0.05, the model is significant.

##g) given the average baby weight is 9 pounds construct 95% confidence interval estimate for the average hours sleep per day formulal = yhat I t critical value * standart error * SQRT ((1/n) + (x-xbar)^2/ssx)) yhat = 14.07146496 t critical value al value 2.446911851 T.INV.2T(0.05,6) SSX 49.08 SUM(X^2) - (SUM(x))^2/8 xbar 9.95 consider S = SQRT((1/n) + (x -xbar)^2 / ssx)) 0.378549865 se = standard error of the model: 0.505952412 lower limit 13.60281229 upper limit 14.54011762 95% confidence interval for Ely) xp is 13.60 to 14.54