nspection trials are carried out in a factory to assess the quality of products. In each trial r; products are tested and Y;, the Bin(ri, p), where p is the umber of satisfactory items in the trial, is assumed to follow the binomial model Y₁ roportion of satisfactory items in the production process. Using inspection data (r₁, y₁), (r2, y2), ..., (rn, Yn) and assuming independent trials, the following log-likelihood for p was obtained 1(p; data)= 19.5678 +40 log(p) + 10 · log(1 − p). ).

The least-squares regression output reports the p-value for a two-sided hypothesis test. True False

Consider the table below which displays the price of a commodity for six consecutive years.   Year Price (dollars) 1 250 2 255 3 253 4 255 5 259 6 261   Use the method of least squares to fit the model E(Yt) = β0+ β1t to the data. Write the prediction equation. Use the prediction equation to obtain forecasts of the prices in years 7 and 8. Find 95% prediction intervals for years 7 and 8.

2. The scatterplot below summarizes husbands' and wives' heights in a random sample of 170 married couples in Britain, where both partners' ages are below 65 years. Summary output of the least squares fit for predicting wife's height from husband's height is also provided in the table. Wife's height (in inches) 70 65 60 55 60 65 70 Husband's height (in inches) 75 (Intercept) height husband Estimate Std. Error 43.5755 4.6842 0.2863 0.0686 t value 9.30 4.17 Pr>t) 0.0000 0.0000 Is there strong evidence that taller men marry taller women? State the hypotheses and include any information used to conduct the test... b) Given that R² = 0.09, what is the correlation of heights in this data set? c) You meet a married man from Britain who is 5'9" (69 inches). What would you predict his wife's height to he? How reliable is this prediction? d) You meet another married Brit who is 6'7" (79 inches). Would it be wise to use the same linear model to predict his wife's height? Why or why not?