a. An experiment was performed on a certainmetal to determine if the strength is a function of heating time(hours). Results based on 25 metal sheets are given below. Use thesimple linear regression model.
?X = 50
?X2 = 200
?Y = 75
?Y2 = 1600
?XY = 400
Find the estimated y intercept and slope. Write the equation of theleast squares regression line and explain the coefficients.Estimate Y when X is equal to 4 hours. Also determine the standarderror, the Mean Square Error, the coefficient of determination andthe coefficient of correlation. Check the relation betweencorrelation coefficient and Coefficient of Determination. Test thesignificance of the slope.
b. Consumer Reports provided extensivetesting and ratings for more than 100 HDTVs. An overall score,based primarily on picture quality, was developed for each model.In general, a higher overall score indicates better performance.The following (hypothetical) data show the price and overall scorefor the ten 42-inch plasma televisions (Consumer Reportdata slightly changed here):
Brand | Price (X) | Score (Y) |
Dell | 3800 | 50 |
Hisense | 2800 | 45 |
Hitachi | 2700 | 35 |
JVC | 3000 | 40 |
LG | 3500 | 45 |
Maxent | 2000 | 28 |
Panasonic | 4000 | 57 |
Phillips | 3200 | 48 |
Proview | 2000 | 22 |
Samsung | 3000 | 30 |
Use the above data to develop and estimated regression equation.Compute Coefficient of Determination and correlation coefficientand show their relation. Interpret the explanatory power of themodel. Estimate the overall score for a 42-inch plasma televisionwith a price of $3600 and perform significance test for theslope.
